<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   FORM 10-Q

                 QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF
                      THE SECURITIES EXCHANGE ACT OF 1934

For the Quarter ended March 31, 1998            Commission File Number  0-1227
                      --------------

                         CHICAGO RIVET & MACHINE CO.
                         ---------------------------
            (Exact name of registrant as specified in its charter)


ILLINOIS                                                            36-0904920  
(State or other jurisdiction of           (I.R.S. Employer Identification No.)
incorporation or organization)

P. O. Box 3061
90l Frontenac Road
Naperville, Illinois                                                   60566
--------------------                                                   -----
(Address of principal executive office)                             (Zip Code)  


Registrant's telephone number, including area code (630)357-8500
                                                   -------------

Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.


Yes    X                   No 
      ---                       ---


Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

Class                                           Outstanding at March 31, 1998
-----                                           -----------------------------

COMMON STOCK, $1.00 PAR VALUE                          1,169,096 SHARES
-----------------------------                          ----------------


DOCUMENTS INCORPORATED BY REFERENCE
-----------------------------------

(1)  Portions of the Company's Interim Report to Shareholders for the Quarter
ended March 31, 1998 are incorporated by reference in Part I of this Report.


<PAGE>   2


                         CHICAGO RIVET & MACHINE CO.

                                    INDEX

<TABLE>
<CAPTION>

PART I.             FINANCIAL INFORMATION                          Page No.
<S>                                                                <C>
      Consolidated Balance Sheets at March 31, 1998 
           and December 31, 1997.                                     2-3

      Consolidated Statements of Operations for the Three
           Months Ended March 31, 1998 and 1997.                        4
      
      Consolidated Statements of Retained Earnings for the
           Three Months Ended March 31, 1998 and 1997.                  5
      
      Consolidated Statements of Cash Flows for the Three
           Months Ended March 31, 1998 and 1997.                        6
      
      Notes to the Consolidated Financial Statements                  7-8
      
      Management's Discussion and Analysis of Financial
           Condition and Results of Operations                       9-10


PART II.            OTHER INFORMATION                               11-15
</TABLE>







                                       1


<PAGE>   3


                          CHICAGO RIVET & MACHINE CO.
                          Consolidated Balance Sheets
                      March 31, 1998 and December 31, 1997
                                        
                                     Assets

<TABLE>
<CAPTION>
                                                              March 31,     December 31,
                                                                1998            1997
                                                                ----            ----
                                                            (unaudited)
<S>                                                         <C>             <C>
Current Assets:
  Cash and cash equivalents                                 $ 4,253,374     $ 3,983,471
  Certificate of deposit                                      1,759,038       2,867,715
  Accounts receivable - net of allowances                     6,065,401       5,662,538
  Inventories:
    Raw materials                                             2,036,996       1,901,419
    Work in process                                           1,514,742       1,427,764
    Finished goods                                            3,149,314       3,025,424
                                                             ----------      ----------
  Total inventories                                           6,701,052       6,354,607
                                                             ----------      ----------

  Deferred income taxes  (Note 4)                               821,335         764,588

  Other current assets                                          474,696         360,448
                                                             ----------      ----------

Total Current Assets                                         20,074,896      19,993,367
                                                             ----------      ----------

Property, Plant and Equipment
    Land and improvements                                     1,008,901       1,008,901
    Buildings and improvements                                5,504,795       5,501,189
    Production equipment, leased
      machines and other                                     22,135,757      21,404,751
                                                             ----------      ----------
                                                             28,649,453      27,914,841
Less - Accumulated Depreciation                              15,312,594      14,960,748
                                                             ----------      ----------
Net Property, Plant and Equipment                            13,336,859      12,954,093
                                                             ----------      ----------

Total Assets                                                $33,411,755     $32,947,460
                                                             ==========      ==========
</TABLE>



See Notes to the Consolidated Financial Statements







                                       2
<PAGE>   4



                          CHICAGO RIVET & MACHINE CO.
                          Consolidated Balance Sheets
                      March 31, 1998 and December 31, 1997
                                        
                      Liabilities and Shareholders' Equity

<TABLE>
<CAPTION>
                                                        March 31,        December 31,
                                                          1998               1997
                                                          ----               ----
                                                       (unaudited)
<S>                                                    <C>               <C>
Current Liabilities:
   Accounts payable                                    $ 2,141,659       $ 1,700,296
   Contributions due profit sharing
     and pension plans                                     160,161           707,747
   Wages and salaries                                    1,066,376           772,247
   Other accrued expenses (Note 5)                         454,167           329,708
   Unearned lease revenue                                   43,964            68,711
   Current portion of note payable                       1,800,000         1,800,000
   Accrued interest expense                                139,721           108,634
   Federal and state income taxes                        1,038,658           739,343
                                                        ----------        ----------
Total Current Liabilities                                6,844,706         6,226,686

Note payable                                             4,500,000         4,950,000
Deferred income taxes (Note 4)                           1,325,811         1,259,672
                                                        ----------        ----------

Total Liabilities                                       12,670,517        12,436,358
                                                        ----------        ----------

Shareholders' Equity:
   Preferred stock, no par value:
     authorized 500,000 shares -
     none outstanding                                        ----              ----
  
   Common stock, $1.00 par value:
     authorized 4,000,000 shares -
     issued and outstanding 1,169,096
     and 1,169,296, respectively                         1,169,096         1,169,296

   Additional paid - in capital                            459,309           459,388
   Retained earnings                                    19,112,833        18,882,418
                                                        ----------        ----------
Total Shareholders' Equity                              20,741,238        20,511,102
                                                        ----------        ----------
Commitments and Contingencies (Note 3)                       ----              ----
                                                        ----------        ----------
Total Liabilities and Shareholders' Equity             $33,411,755       $32,947,460
                                                        ==========        ==========
</TABLE>


See Notes to the Consolidated Financial Statements






                                       3


<PAGE>   5


                          CHICAGO RIVET & MACHINE CO.
                     Consolidated Statements of Operations
               For the Three Months Ended March 31, 1998 and 1997
                                  (unaudited)


<TABLE>
<CAPTION>    
                                                      Three Months Ended
                                                          March 31,
                                                    1998              1997
                                                    ----              ----
<S>                                             <C>                <C>
Net sales                                       $11,580,739        $11,803,592
Lease revenue                                        92,210             95,053
                                                 ----------         ----------
                                                 11,672,949         11,898,645
Cost of goods sold and costs
 related to lease revenue                         8,271,340          8,790,141
                                                 ----------         ----------
Gross profit                                      3,401,609          3,108,504
Shipping, selling and
 administrative expenses                          1,822,305          1,702,113
Profit sharing and pension
 expenses                                           120,299            140,000
                                                 ----------         ----------
                                                  1,459,005          1,266,391

Other income and expenses:
Interest income from
 U.S. government securities
 and certificates of deposit                         83,982             34,769
Interest expense                                   (105,525)          (135,138)
Gain from sale of leased
 machines and other equipment                        14,311              1,500
Amortization expense                                   ---              (6,249)
Other income, net of other expense                  (26,953)             4,710
                                                 ----------         ----------
Income before income taxes                        1,424,820          1,165,983
Provision for income taxes                          510,000            434,000
                                                 ----------         ----------
Net income                                      $   914,820        $   731,983
                                                 ==========         ==========
Average common shares outstanding                 1,169,100          1,171,496
                                                 ==========         ==========
Per share data:

   Net income per share                         $       .78        $       .62
                                                 ==========         ==========
   Cash dividends declared per share            $       .58        $       .40
                                                 ==========         ==========
</TABLE>


See Notes to the Consolidated Financial Statements





                                       4

<PAGE>   6


CHICAGO RIVET & MACHINE CO.
Consolidated Statements of Retained Earnings
For the Three Months Ended March 31, 1998 and 1997
(unaudited)


<TABLE>
<CAPTION>
                                                            March 31,

                                                      1998             1997
                                                      ----             ----
<S>                                                <C>              <C>
Retained earnings at beginning
   of period                                       $18,882,418      $16,145,012


Net income for the three months ended                  914,820          731,983

Treasury stock retired at cost                          (5,371)             ---


Cash dividends declared in the period -
   $.58 per share in 1998 and $.40 per
   share in 1997.                                     (679,034)        (468,594)
                                                    ----------       ----------

Retained earnings at end of period                 $19,112,833      $16,408,401
                                                    ==========       ==========
</TABLE>









See Notes to the Consolidated Financial Statements






                                       5




<PAGE>   7

CHICAGO RIVET & MACHINE CO.
Consolidated Statements of Cash Flows
For the Three Months Ended March 31, 1998 and 1997
(unaudited)

<TABLE>
<CAPTION>
                                                                     March 31,           March 31,
                                                                       1998                1997
                                                                       ----                ----
<S>                                                                 <C>                 <C> 
Cash flows from operating activities:
Net income                                                          $  914,820          $  731,983
Adjustments to reconcile net income to net cash
 provided by operating activities:
   Depreciation and amortization                                       374,071             340,968
   Net gain on the sale of properties                                  (14,311)             (1,500)
   Deferred income taxes                                                 9,392              33,625
   Changes in current assets and current liabilities:
     Accounts receivable, net                                         (402,863)           (654,776)
     Inventories                                                      (346,445)            703,055
     Accounts payable                                                  (26,910)           (164,401)
     Accrued interest                                                   31,087              (2,362)
     Other accrued expenses                                            124,459              62,976
     Accrued wages and salaries                                        294,129             245,663
     Accrued profit sharing                                           (547,586)           (197,301)
     Taxes payable                                                     299,315             303,875
     Other, net                                                       (138,998)            (41,269)
                                                                     ---------           ---------
   Net cash provided by operating activities                           570,160           1,360,536
                                                                     ---------           ---------
Cash flows from investing activities:
   Capital expenditures                                               (761,329)           (132,861)
   Net proceeds from the sale of properties                             18,806              12,546
   Proceeds from held-to-maturity securities                         2,467,715             937,220
   Purchases of held-to-maturity securities                         (1,359,038)           (880,361)
                                                                     ---------           ---------
   Net cash provided (used) by investing activities                    366,154             (63,456)
                                                                     ---------           ---------
Cash flows from financing activities:
   Payments under term loan agreement                                 (450,000)           (450,000)
   Purchase of treasury stock                                           (5,650)               ---
   Cash dividends                                                     (210,761)           (175,724)
                                                                     ---------           ---------
   Net cash used by financing activities                              (666,411)           (625,724)
                                                                     ---------           ---------
Net increase in cash and cash equivalents                              269,903             671,356
Cash and cash equivalents at beginning
 of period                                                           3,983,471           3,215,688
                                                                     ---------           ---------
Cash and cash equivalents at end of period                          $4,253,374          $3,887,044
                                                                     =========           =========
Cash paid during the period for:     
   Income taxes                                                     $  201,293          $   96,500
   Interest                                                         $  105,060          $  135,138
</TABLE>

See Notes to the Consolidated Financial Statements






                                       6

<PAGE>   8

CHICAGO RIVET & MACHINE CO.

NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS
(Unaudited)


1. In the opinion of the Company, the accompanying unaudited financial
statements contain all adjustments necessary to present fairly the financial
position of the Company as of March 31, 1998 and December 31, 1997 and the
results of operations and changes in cash flow for the indicated periods.

The Company uses estimated gross profit rates to determine the cost of goods
sold during interim periods. Actual results could differ from those estimates
and will be adjusted, as necessary, following the Company's annual physical
inventory in the fourth quarter.

The preparation of financial statements in conformity with generally accepted
accounting principles requires management to make estimates and assumptions
that affect the reported amounts of assets and liabilities and disclosure of
contingent assets and liabilities at the date of the financial statements and
the reported amounts of revenues and expenses during the reporting period.
Actual results could differ from those estimates.

2. The results of operations for the three month period ending March 31, 1998
are not necessarily indicative of the results to be expected for the year.

3. The Company is, from time to time, involved in litigation, including
environmental claims, in the normal course of business.  With regard to
environmental claims, the Company  has been named by state and/or  federal
government agencies as a "potentially responsible party"  with respect to
certain waste disposal sites.  As a potentially responsible party, the Company
may be considered jointly and severally liable, along with other potentially
responsible parties, for the cost of remediation of  these waste sites. Certain
estimates related to remediation costs were favorably adjusted during 1997 as
remediation work nears completion at certain sites, while claims at other  sites
are nearing resolution, and, accordingly, the Company has revised the amount of
reserves recorded in connection with these claims.  The actual cost of
remediation is presently unknown; however, estimates currently available suggest
that the remaining cost of  remediation at these sites will be between $33
million and $49 million. Despite the joint and several nature of liability,
these proceedings are frequently resolved on the basis of the quantity and type
of waste disposed by the parties.  The actual amount of liability for the
Company is unknown due to disagreement  concerning the allocation of
responsibility, uncertainties regarding the amount of contribution that will be
available from other parties and uncertainties related to insurance coverage.
After investigation of the quantities and type of waste disposed at these sites,
it is management's opinion that any liability will not be material to the
Company's financial condition.  Nevertheless, it is likely that the Company will
incur additional  costs associated with these proceedings, and, accordingly, the
Company has recorded a total liability of $84,000 related to these matters.  The
adequacy of this reserve will be reviewed periodically as more definitive cost
information becomes available.

In the normal course of business the Company extends credit primarily on the
basis of 30 day terms to various customers, principally, in the automotive
industry in the Midwestern United States. Currently, the Company is
re-negotiating payment terms with a certain customer representing approximately
10% of the March 31, 1998 consolidated accounts receivable balance. Management
believes that the situation will be successfully resolved and substantially all
of the account balance will be collected during the remainder of 1998.
Management is of the opinion that existing reserves are adequate, accordingly
no additional loss provisions have been made at this time. The situation will
be monitored and reviewed as more information becomes available.



                                       7







<PAGE>   9



CHICAGO RIVET & MACHINE CO.
NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS (CON'T.)
(Unaudited)


4. At March 31, 1998 significant deferred tax liabilities and assets were
comprised of the following:

<TABLE>
                <S>                                    <C>
                Depreciation                           $ (1,325,811)
                                                        -----------
                                                         (1,325,811)

                Environmental accruals                       47,015
                Inventory valuations                        427,166
                Accrued vacation                            225,935
                Doubtful accounts                            53,986
                Unearned rental revenue                      17,586
                Other, net                                   49,647
                                                        -----------
                                                            821,335
                                                        -----------
                                                       $   (504,476)
                                                        ===========
</TABLE>

5. Other Accrued Expenses - accrued expenses consist of the following:

<TABLE>
<CAPTION>
                                March 31, 1998     December 31, 1997
                                --------------     -----------------
      <S>                       <C>                <C>
      Environmental costs            $  83,538            $  85,000
      Property taxes                   128,927               95,620
      Payroll taxes                     85,472               68,951
      All other items                  156,230               80,137
                                       -------              -------
                                     $ 454,167            $ 329,708
                                       =======              =======
</TABLE>

6. The Company extends credit primarily on the basis of 30 day terms to various
companies doing business primarily in the automotive and appliance industries.
The Company has a concentration of credit risk primarily within the automotive
industry and in the Midwestern United States.






                                       8


<PAGE>   10

CHICAGO RIVET & MACHINE CO.
Management's Discussion and Analysis of Financial Condition and Results of
Operations

     The Company enjoyed a successful first quarter in 1998, posting  an
increase in net income despite a modest decline in revenues.  Net sales and
lease revenues amounted to $11,672,949 compared to $11,898,645 recorded during
the first quarter of 1997.  Revenues related to the sale of fasteners and
cold-formed products increased compared to the first quarter of 1997 as demand
for these products remained relatively high.  Those gains were offset by lower
revenues from the sale of automatic assembly equipment.  Demand in this segment
has not been as strong as in the prior period, and, based upon recent activity,
we do not anticipate that demand will increase in the near future.
     We are pleased to report that net income improved to $914,820, or $.78 per
share on 1,169,100 average shares outstanding.  It should be noted that net
income during the first quarter of 1997 was reduced by approximately $.18 per
share due to certain accounting conventions, and conservative estimates,
associated with purchase accounting in connection with the acquisition of H & L
Tool Company that occurred in the fourth quarter of 1996.  Therefore,  on an
adjusted basis, earnings for both periods are approximately equal, despite
marginally lower sales levels and a less favorable product mix in the first
quarter of 1998.
     Selling, general and administrative expenses increased by approximately
$120,000 compared to the first quarter of 1997.  Most of this change is due to
expenses associated with the implementation of the new management information
system, including third party consulting and the utilization of temporary,
contract technical support personnel.
     The Company's financial condition continues to be sound.  During the
quarter, working capital declined approximately $.6 million, but still totaled
approximately $13.2 million, which represents an increase of  nearly $1.0
million compared with the first quarter of 1997.  The Company took delivery of
new cold-heading equipment, valued at $719,000 during the first quarter of 1998
and this was the single largest factor contributing to the change in working
capital compared to year end 1997.  Accounts receivable increased compared to
the year end balances, largely due to an increase in sales during the first
quarter compared with the fourth quarter of 1997.  The level of inventories
also increased somewhat compared to year end 1997,  but the investment in
inventories is expected to decline to more normal levels in the months ahead.
     Late in 1996, in connection with the purchase of H & L Tool, the Company
borrowed $9.0 million, on an unsecured basis, subject to certain customary
covenants.  Under the terms of the note evidencing such debt, the Company will
repay the principal in 20 quarterly installments of $450,000, plus interest
computed on the unpaid balance at a variable rate that is calculated under one
of two methods: the LIBOR rate plus 80 basis points; or the lender's reference
rate, less 75 basis points.  The rate is adjusted quarterly and at the end of
the first quarter of 1998 was  approximately 6.6%.  The Company is in full
compliance with all terms of the note and, during 1997, made an extra payment
of $450,000 against the principal balance of the note.  At the end of the first
quarter of 1998, the balance due was $6.3 million.  Also in connection with the
acquisition of H & L Tool, the Company obtained a $1.0 million line of credit
from the Bank of America.  This line remains unused and is scheduled to expire
on May 30, 1998.  Although the Company believes that its existing cash, cash
equivalents and existing borrowings will be sufficient to provide adequate
working capital through at least the next twelve months, consideration will be
given to extending the line of credit for an additional twelve months.



                                       9

<PAGE>   11


     Overall, we continue to be pleased with results.  We remain focused on our
core operations, with an emphasis on cost control and operating improvements.
Our quality and service initiatives are on schedule:  a second facility
recently received accreditation to the coveted QS9000 standard and a third
facility has been recommended for registration.  Our backlog of open orders is
not as large as one year ago, and incoming orders are not quite as strong as
those enjoyed a year ago, but we believe that business will remain strong
enough to maintain operations for the foreseeable future.  We continue to
solicit new business from customers, and potential customers, in a variety of
industries, but our primary market continues to be centered around the
automobile industry, and our level of operations remain very closely tied to
the level of activity in that sector of the economy.

This discussion contains certain "forward-looking statements" which are
inherently subject to risks and uncertainties that may cause actual events to
differ materially from those discussed herein.  Factors which may cause such
differences in events include, among other things, fluctuations in general
economic conditions, consumer demand, the gain or loss of a key customer, and
the price and availability of  the Company's primary raw materials.  Therefore,
readers are cautioned not to place undue reliance upon such forward-looking
statements.














                                       10

<PAGE>   12



PART II  --  OTHER INFORMATION

Item 6.  Exhibits and Reports on Form 8-K

         (a)  Exhibits

              19.1  Interim Report to Shareholders for the quarter ended 
                    March 31, 1998.

              27.1  Financial Data Schedule.

         (b)  Reports on Form 8-K

              No reports on Form 8-K were filed during the current period.


SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                            CHICAGO RIVET & MACHINE CO.
                                                   (Registrant)

Date:  May 14, 1998
                                            /s/         John A. Morrissey
                                                        John A. Morrissey
                                       Chairman of the Board of Directors
                                        and Chief Executive Officer


Date:  May 14, 1998
                                            /s/         John C. Osterman
                                                        John C. Osterman
                                       President, Chief Operating
                                        Officer and Treasurer (Principal
                                                       Financial Officer)


Date:  May 14, 1998
                                            /s/          Stephen D. Voss
                                                         Stephen D. Voss
                                      Assistant Treasurer and Controller







                                       11
<PAGE>   13


CHICAGO RIVET & MACHINE CO.

EXHIBITS


INDEX TO EXHIBITS


Exhibit
Number                                                                 Page

  19.1             Interim Report to Shareholders for the
                    quarter ended March 31, 1998.                     13 - 14

  27.1             Financial Data Schedule                                 15















                                       12