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                                                                    Exhibit 99.1

                          Description of Capital Stock

     The following description of our capital stock is qualified in its entirety
by reference to our Amended and Restated Certificate of Incorporation filed with
the Delaware Secretary of State on August 21, 2002 (our "Certificate of
Incorporation"), our Amended and Restated Bylaws dated March 7, 2002 (our
"Bylaws"), the Rights Agreement between us and The Bank of New York, as Rights
Agent, dated December 8, 1995, as amended (the "Rights Agreement"), and the
warrants issued to Occidental Chemical Holding Corporation ("OCHC") on August
22, 2002 (the "Warrants").

     Our authorized capital stock consists of 500,000,000 shares divided into
two class as follows:

     .  420,000,000 shares of common stock issued in two series with the first
        consisting of 340,000,000 shares of common stock, par value $1 per share
        ("Common Stock") and the second series consisting of 80,000,000 shares
        of Series B Common Stock, par value $1 per share ("Series B Common
        Stock"); and

     .  80,000,000 shares of preferred stock, par value $.01 per share
        ("Preferred Stock").

Common Stock

     The holders of our Common Stock and Series B Common Stock are entitled to
one vote per share on all matters to be voted on by stockholders generally,
including the election of directors. Except as otherwise provided for in our
Certificate of Incorporation or by Delaware law, holders of shares of Common
Stock and holders of shares of Series B Common Stock vote together as a single
class. There are no cumulative voting rights, meaning that the holders of a
majority of the shares voting for the election of directors can elect all of the
directors standing for election. Our Certificate of Incorporation provides that
any action required or permitted to be taken by the stockholders may be effected
either at a duly called annual or special meeting of the stockholders or by
consent in writing by such holders.

     Our Certificate of Incorporation provides that in the case of
reorganizations, consolidations or mergers, holders of shares of Common Stock
and Series B Common Stock must receive the same kind and amount of securities or
property upon the reorganization, consolidation or merger, except as otherwise
approved by the affirmative vote of a majority of the outstanding shares of each
of the Common Stock and Series B Common Stock, voting as separate classes. This
requirement does not apply to mergers solely for the purpose of forming a
holding company if specified requirements are met or to reorganizations,
consolidations or mergers where Lyondell Chemical Company is the continuing
corporation and which do not result in any distribution to our stockholders or
reclassification or change in the outstanding Common Stock or Series B Common
Stock. Our Certificate of Incorporation also provides that any proposal to alter
in an adverse manner the powers, preferences or rights of shares of Series B

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Common Stock requires the affirmative vote of 80% of the outstanding shares of
Series B Common Stock. Any proposal to alter in an adverse manner the powers,
preferences or rights of shares of Common Stock requires the affirmative vote of
a majority of the outstanding shares of Common Stock. Any increase in the
authorized number of shares of any class or classes of our stock, or the
creation, authorization or issuance of any securities convertible into, or
warrants, options or similar rights to purchase, acquire or receive, shares of
any such class or classes of stock, are deemed not to adversely affect the
powers, preferences or special rights of the shares of either the Common Stock
or the Series B Common Stock.

     Our Common Stock and Series B Common Stock do not carry any preemptive or
other subscription rights to purchase shares of our stock and are not entitled
to the benefits of any sinking fund. Our Common Stock is not convertible and
neither our Common Stock nor our Series B Common Stock are redeemable or
assessable. Our Series B Common Stock may be converted into shares of Common
Stock at any time at our option or the option of the holder (subject to certain
contractual limitations).

     If we are liquidated, dissolved or wound up, holders of our Common Stock
and Series B Common Stock would be entitled to share ratably in all of our
assets and properties available for distribution to the holders of Common Stock
and Series B Common Stock after payment has been made or set aside in the full
amount necessary to satisfy any preferential or participating rights to which
holders of each outstanding series of Preferred Stock are entitled.

     Holders of Common Stock and Series B Common Stock are entitled to receive
such dividends as may from time to time be declared by our Board of Directors.
Our Board of Directors may not declare a dividend on shares of Common Stock
without also declaring a dividend in the same amount and form on shares of
Series B Common Stock. However, if our Board of Directors declares a cash
dividend on shares of Common Stock, it may in its sole discretion declare and
pay a dividend on shares of Series B Common Stock by issuance of additional
shares of Series B Common Stock to the holders thereof in lieu of cash. In that
event, the number of shares of Series B Common Stock to be issued as a dividend
will be determined pursuant to a formula set forth in our Certificate of
Incorporation.

     Shares of Common Stock and Series B Common Stock are not liable to further
calls or assessments by us for any of our liabilities that may be imposed on our
stockholders under the laws of the State of Delaware, our state of
incorporation.

Preferred Stock

     Our Board of Directors has the authority, without stockholder approval, to
issue shares of Preferred Stock in one or more series and to fix the number of
shares and terms of each series. The Board may determine the designation and
other terms of each series, including, among others:

     . dividend rights;

     . voting powers;

     . preemptive rights;


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     . conversion rights;
     . redemption rights; and
     . liquidation preferences.

     The issuance of Preferred Stock, while providing desired flexibility in
connection with possible acquisitions and other corporate purposes, could
adversely affect the voting power of our holders of Common Stock and Series B
Common Stock. It also could affect the likelihood that holders of our Common
Stock and Series B Common Stock will receive dividend payments and payments upon
liquidation.

Warrants

     We issued five million Warrants to OCHC. Each of the Warrants is
exercisable for the purchase of one share of our Common Stock, at an exercise
price of $25 per share, on or before the expiration date of the Warrants on
August 22, 2007. Upon exercise, however, we have the right, in our sole
discretion, to instead make a "Net Payment" by electing to pay the excess, if
any, between the stock price per share of Common Stock on the date of exercise
and the $25 exercise price. The Net Payment may be in the form of (i) cash, (ii)
shares of Common Stock, (iii) subject to specified limitations, shares of Series
B Common Stock or (iv) a combination of (i), (ii) and (iii), at our option. If
we elect to make all or a portion of a Net Payment in the form of shares of
Common Stock or Series B Common Stock, each share will be valued by the average
of the high and low per-share sale prices of Common Stock, as reported on the
New York Stock Exchange, on the date a Warrant is exercised.

     The number of Warrants and the exercise price may be adjusted on December
31, 2002 based upon the average of the high and low per-share sale prices of
Common Stock, as reported on the New York Stock Exchange, for the 15
business-day period ending December 31, 2002. If the 15 business-day average
price on December 31, 2002 is $11.00 or above, the Warrant will not be adjusted.
If the 15 business-day average price on that day is between $7.00 and $11.00:
(1) the number of Warrants will be determined by adding to five million the
number computed by multiplying (a) $11.00 minus the 15 business-day average
stock price, by (b) 250,000; and (2) the exercise price will be determined by
subtracting from $25.00 the number computed by multiplying (x) $11.00 minus the
15 business-day average stock price, by (y) $0.675. If the 15 business-day
average price on that day is $7.00 or below: (1) the number of Warrants will be
increased to six million; and (2) the exercise price will be reduced to $22.30
per share. The number of Warrants and the exercise price will also be adjusted
for any stock splits, dividends and combinations that occur during the five-year
exercise period.

     Transfer of the Warrants is restricted by agreement among us and OCHC and
its parent, Occidental Petroleum Corporation.

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Provisions of Our Bylaws

     Certain provisions of our Bylaws establish time periods during which
appropriate stockholder proposals must be delivered to us for consideration at
special and annual meetings called by us. Our Bylaws provide, among other
things, that stockholders making nominations for our Board of Directors at, or
bringing other business before, an annual or a special meeting of stockholders
must provide timely written notice to us thereof, timely notice being required
to be no later than 90 days in advance of the meeting. However, if the date of
the meeting was not publicly announced by a mailing to stockholders, in a press
release reported by the Dow Jones News Services, Associated Press or comparable
national news service or in a filing with the Securities and Exchange Commission
pursuant to Section 13, 14 or 15(d) of the Securities Exchange Act of 1934 more
than 90 days prior to the meeting, such notice, to be timely, must be delivered
to our Board of Directors not later than the close of business on the tenth day
following the day on which the date of the meeting was first so publicly
announced.

Anti-Takeover Provisions of Our Certificate of Incorporation

     Our Certificate of Incorporation contains provisions that could delay or
make more difficult the acquisition of control of Lyondell Chemical Company
through a hostile tender offer, open market purchases, proxy contest, merger or
other takeover attempt, including those attempts that might result in a premium
over the market price of our Common Stock.

     We have 420,000,000 authorized shares of common stock and 80,000,000
authorized shares of Preferred Stock. One of the consequences of our authorized
but unissued common stock and undesignated Preferred Stock may be to enable our
Board of Directors to make more difficult or to discourage an attempt to obtain
control of us. If, in the exercise of its fiduciary obligations, our Board of
Directors determined that a takeover proposal was not in our best interest, the
Board could authorize the issuance of those shares without stockholder approval.
The shares could be issued in one or more transactions that might prevent or
make the completion of the change of control transaction more difficult or
costly by:

     . diluting the voting or other rights of the proposed acquiror or insurgent
       stockholder group;
     . creating a substantial voting block in institutional or other hands that
       might undertake to support the position of the incumbent Board; or
     . effecting an acquisition that might complicate or preclude the takeover.

     In this regard, while our Certificate of Incorporation grants our Board of
Directors broad power to establish the rights and preferences of the authorized
and unissued Preferred Stock, our Board of Directors has adopted a policy
providing that no future issuance of Preferred Stock will be effected without
the approval of the holders of our Common Stock unless our Board of Directors
(whose decision shall be conclusive) determines in good faith:

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     . that the issuance is primarily for the purpose of facilitating a
       financing, an acquisition or another proper corporate objective or
       transaction; and

     . that any anti-takeover effects of the issuance are not our primary
       purpose for effecting such issuance.

Our Board of Directors will not amend or revoke this policy without giving
written notice to the holders of all outstanding shares of our stock. However,
no such amendment or revocation will be effective, without the approval of the
holders of our Common Stock, to permit a subsequent issuance of Preferred Stock
for the primary purpose of obstructing a takeover of Lyondell Chemical Company
by any person who has, prior to such written notice to stockholders, notified
the Board of Directors of its desire to pursue a takeover of Lyondell Chemical
Company.

Delaware Anti-Takeover Law

     We are a Delaware corporation and are subject to Section 203 of the
Delaware General Corporation Law, which regulates corporate acquisitions.
Section 203 prevents an "interested stockholder," which is defined generally as
a person owning 15% or more of a corporation's voting stock, or any affiliate or
associate of that person, from engaging in a broad range of "business
combinations" with the corporation for three years after becoming an interested
stockholder unless:

     . the board of directors of the corporation had previously approved either
       the business combination or the transaction that resulted in the
       stockholder's becoming an interested stockholder;
     . upon completion of the transaction that resulted in the stockholder's
       becoming an interested stockholder, that person owned at least 85% of the
       voting stock of the corporation outstanding at the time the transaction
       commenced, excluding shares owned by persons who are directors and also
       officers and shares owned in employee stock plans in which participants
       do not have the right to determine confidentially whether shares held
       subject to the plan will be tendered; or
     . following the transaction in which that person became an interested
       stockholder, the business combination is approved by the board of
       directors of the corporation and holders of at least two-thirds of the
       outstanding voting stock not owned by the interested stockholder.

     Under Section 203, the restrictions described above also do not apply to
specific business combinations proposed by an interested stockholder following
the announcement or notification of designated extraordinary transactions
involving the corporation and a person who had not been an interested
stockholder during the previous three years or who became an interested
stockholder with the approval of a majority of the corporation's directors, if
such extraordinary transaction is approved or not opposed by a majority of the
directors who were directors prior to any person becoming an interested
stockholder during the previous three years or were recommended for election or
elected to succeed such directors by a majority of such directors. Section 203
may make it more difficult for a person who would be an interested stockholder
to effect various business combinations with a corporation for a three-year
period.

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Limitation on Directors' and Officers' Liability

     Section 102(b)(7) of the Delaware General Corporation Law permits a
corporation to provide in its certificate of incorporation that a director of
the corporation shall not be personally liable to the corporation or its
stockholders for monetary damages for breach of fiduciary duty as a director,
except for liability for any of the following:

     . any breach of the director's duty of loyalty to the corporation or its
       stockholders,
     . acts or omissions not in good faith or which involve intentional
       misconduct or a knowing violation of law,
     . payments of unlawful dividends or unlawful stock repurchases or
       redemptions, or
     . any transaction from which the director derived an improper personal
       benefit.

     Any repeal or modification of such provisions shall not adversely affect
any right or protection of a director for or with respect to any acts or
omissions of such director occurring prior to such amendment or repeal. Our
Certificate of Incorporation provides that no director shall be personally
liable to us or any of our stockholders for monetary damages for breach of
fiduciary duty as a director to the fullest extent permitted by Delaware law.
The inclusion of this provision in our Certificate of Incorporation may have the
effect of reducing the likelihood of derivative litigation against directors and
may discourage or deter stockholders or management from bringing a lawsuit
against directors for breach of their duty of care, even though such an action,
if successful, might otherwise have benefited us and the holders of our Common
Stock and Series B Common Stock.

Rights Plan

     Our Board of Directors declared a dividend of one right ("Right") for each
outstanding share of our Common Stock to stockholders of record at the close of
business on December 20, 1995 and all shares of Common Stock and Series B Common
Stock issued thereafter are issued with such Right. Each Right entitles the
registered holder to purchase from us one share of Common Stock at a purchase
price of $80 per share of Common Stock, subject to adjustment (the "Purchase
Price"). The description and terms of the Rights are set forth in the Rights
Agreement. Initially, the Rights will be attached to all certificates
representing outstanding Common Equity (as defined below) and no separate
certificates for the Rights ("Rights Certificates") will be distributed. "Common
Equity" means shares of Common Stock and Series B Common Stock and any other
series of our common stock issued and outstanding after December 20, 1995 and
prior to the earlier of the Distribution Date (as defined below) or the
Expiration Date (as defined in the Rights Agreement). The Rights will separate
from the Common Equity and a "Distribution Date" will occur, with certain
exceptions, upon the earlier of (i) ten days following a public announcement of
the existence of an "Acquiring Person" (the date of the announcement being the
"Stock Acquisition Date"), or (ii) ten business days following the commencement
of a tender offer or exchange offer that would result in a person's becoming an
Acquiring Person. An "Acquiring Person" is any person or group of affiliated or
associated persons that has acquired or obtained the right to acquire beneficial
ownership of 15%

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or more of the outstanding shares of Common Equity, except that our Board of
Directors has adopted a resolution pursuant to the terms of the Rights Agreement
that provides that OCHC and its Affiliates (as defined in the Rights Agreement)
and Associates (as defined in the Rights Agreement) will not be or become an
"Acquiring Person" unless and until such time as OCHC together with its
Affiliates and Associates acquires or becomes the beneficial owner of more than
40% of the outstanding Common Equity so long as OCHC's beneficial ownership is
the result of (i) transactions contemplated by the Securities Purchase Agreement
dated July 8, 2002 between us and OCHC or (ii) a reduction in the number of
shares of Common Equity outstanding due to the repurchase of our Common Equity.
In certain circumstances prior to the time a person has become an Acquiring
Person, the Distribution Date may be deferred by the Board of Directors. Certain
inadvertent acquisitions will not result in a person becoming an Acquiring
Person if the person promptly divests itself of sufficient Common Equity. Until
the Distribution Date, (a) the Rights will be evidenced by the Common Equity
certificates (together with this Description of Capital Stock or bearing the
notation referred to below) and will be transferred with and only with such
Common Equity certificates, (b) Common Equity certificates issued after December
20, 1995 will contain a notation incorporating the Rights Agreement by reference
and (c) the surrender for transfer of any certificate for Common Equity (with or
without a copy of this Description of Capital Stock) will also constitute the
transfer of the Rights associated with the Common Equity represented by such
certificate.

     The Rights are not exercisable until the Distribution Date and will expire
at the close of business on December 8, 2005, unless earlier redeemed or
exchanged by us as described below.

     As soon as practicable after the Distribution Date, Rights Certificates
will be mailed to holders of record of Common Equity as of the close of business
on the Distribution Date and, from and after the Distribution Date, the separate
Rights Certificates alone will represent the Rights. All Common Equity issued
prior to the Distribution Date will be issued with Rights. Common Equity issued
after the Distribution Date in connection with certain employee benefit plans or
upon conversion of certain securities will be issued with Rights. Except as
otherwise determined by the Board of Directors, no other shares of Common Equity
issued after the Distribution Date will be issued with Rights.

     In the event (a "Flip-In Event") that a person becomes an Acquiring Person
(except pursuant to a tender or exchange offer for all outstanding shares of
Common Equity at a price and on terms that a majority of our independent
directors determines to be fair to and otherwise in the best interests of us and
our stockholders (a "Permitted Offer")), each holder of a Right will thereafter
have the right to receive, upon exercise of such Right, a number of shares of
Common Equity (or, in certain circumstances, cash, property or other securities
of Lyondell Chemical Company) having a Current Market Price (as defined in the
Rights Agreement) equal to two times the exercise price of the Right.
Notwithstanding the foregoing, following the occurrence of any Flip-In Event,
all Rights that are, or (under certain circumstances specified in the Rights
Agreement) were, beneficially owned by or transferred to such Acquiring Person
(or by certain related parties) will be null and void in the circumstances set
forth in the Rights Agreement.

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     For example, at an exercise price of $80 per Right, each Right not owned by
such an Acquiring Person (or by certain related parties) following an event set
forth in the preceding paragraph would entitle its holder to purchase $160 worth
of Common Stock (or other consideration, as noted above), based upon its then
Current Market Price, for $80. Assuming that the Common Stock had a Current
Market Price of $25 per share at such time, the holder of each valid Right would
be entitled to purchase 6.4 shares of Common Stock for $80.

     In the event (a "Flip-Over Event") that, at any time from and after the
time an Acquiring Person becomes such, (i) we are acquired in a merger or other
business combination transaction (other than certain mergers that follow a
Permitted Offer), or (ii) 50% or more of our assets or earning power is sold or
transferred, each holder of a Right (except Rights owned by such Acquiring
Person or certain related parties) shall thereafter have the right to receive,
upon exercise, a number of shares of common stock of the acquiring company
having a Current Market Price equal to two times the exercise price of the
Right. Flip-In Events and Flip-Over Events are collectively referred to as
"Triggering Events."

     The Purchase Price payable, and the number of shares of Common Stock or
other securities or property issuable, upon exercise of the Rights are subject
to adjustment from time to time to prevent dilution (i) in the event of a stock
dividend on, or a subdivision, combination or reclassification of, the Common
Stock, (ii) if holders of the Common Equity are granted certain rights or
warrants to subscribe for Common Equity or securities convertible into Common
Equity at less than the current market price of the Common Stock, or (iii) upon
the distribution to holders of the Common Equity of evidences of indebtedness or
assets (excluding regular quarterly cash dividends) or of subscription rights or
warrants (other than those referred to above).

     With certain exceptions, no adjustment in the Purchase Price will be
required until cumulative adjustments amount to at least 1% of the Purchase
Price. No fractional shares of Common Stock are required to be issued upon
exercise of the Rights, but in lieu thereof a cash payment may be made based on
the market price of the Common Stock on the last trading date prior to the date
of exercise.

     At any time until the time a person becomes an Acquiring Person, we may
redeem the Rights in whole, but not in part, at a price of $.005 per Right,
payable, at our option, in cash, shares of Common Stock or such other
consideration as our Board of Directors may determine. Immediately upon the
effectiveness of the action of the Board of Directors ordering redemption of the
Rights, the Rights will terminate and the only right of the holders of Rights
will be to receive the $.005 redemption price.

     At any time after the occurrence of a Flip-In Event and prior to the
occurrence of a Flip-Over Event or a person becoming the beneficial owner of 50%
or more of the shares of Common Stock then outstanding, we may exchange the
Rights (other than Rights owned by an Acquiring Person or an affiliate or an
associate of an Acquiring Person, which will have become void), in whole or in
part, at an exchange ratio of one share of Common Stock, and/or other equity

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securities deemed to have the same value as one share of Common Stock, per
Right, subject to adjustment.

     Until a Right is exercised, the holder thereof, as such, will have no
rights as a stockholder, including, without limitation, the right to vote or to
receive dividends. While the distribution of the Rights should not be taxable to
stockholders or us, stockholders may, depending upon the circumstances,
recognize taxable income in the event that the Rights become exercisable for our
Common Stock (or other consideration) or for the common stock of the acquiring
company as set forth above or are exchanged as provided in the preceding
paragraph.

     Other than the redemption price, any of the provisions of the Rights
Agreement may be amended by our Board of Directors as long as the Rights are
redeemable. Thereafter, the provisions of the Rights Agreement (other than the
Redemption Price) may be amended by the Board of Directors in order to cure any
ambiguity, defect or inconsistency, to make changes that do not materially
adversely affect the interests of holders of Rights (excluding the interests of
any Acquiring Person), or to shorten or lengthen any time period under the
Rights Agreement; provided, however, that no amendment to lengthen the time
period governing redemption or amendment shall be made at such time as the
Rights are not redeemable.