<PAGE>
                                                                    EXHIBIT 31-A
                                  CERTIFICATION

I, Lyle G. Heidemann, certify that:

     1.   I have reviewed this annual report on Form 10-K of True Value Company;

     2.   Based on my knowledge, this annual report does not contain any untrue
          statement of a material fact or omit to state a material fact
          necessary to make the statements made, in light of the circumstances
          under which such statements were made, not misleading with respect to
          the period covered by this annual report;

     3.   Based on my knowledge, the financial statements, and other financial
          information included in this annual report, fairly present in all
          material respects the financial condition, results of operations and
          cash flows of True Value as of, and for, the periods presented in this
          annual report;

     4.   True Value's other certifying officer and I are responsible for
          establishing and maintaining disclosure controls and procedures (as
          defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for True Value
          and have:

          a.   designed such disclosure controls and procedures, or caused such
               disclosure controls and procedures to be designed under our
               supervision, to ensure that material information relating to True
               Value, including its consolidated subsidiaries, is made known to
               us by others within those entities, particularly during the
               period in which this annual report is being prepared;

          b.   evaluated the effectiveness of True Value's disclosure controls
               and procedures and presented in this annual report our
               conclusions about the effectiveness of the disclosure controls
               and procedures, as of the end of the period covered by this
               annual report based on such evaluation; and

          c.   disclosed in this annual report any change in True Value's
               internal control over financial reporting that occurred during
               True Value's most recent fiscal quarter (True Value's fourth
               fiscal quarter in the case of an annual report) that has
               materially affected, or is reasonably likely to materially
               affect, True Value's internal control over financial reporting;

     5.   True Value's other certifying officer and I have disclosed, based on
          our most recent evaluation, to True Value's auditors and the audit
          committee of True Value's board of directors:

          a.   all significant deficiencies and material weaknesses in the
               design or operation of internal controls which are reasonably
               likely to adversely affect True Value's ability to record,
               process, summarize and report financial information; and

          b.   any fraud, whether or not material, that involves management or
               other employees who have a significant role in True Value's
               internal control over financial reporting.


                                           TRUE VALUE COMPANY


                                           By: /s/ LYLE G. HEIDEMANN
                                           -------------------------

                                           Lyle G. Heidemann
                                           President and Chief Executive Officer


Date: March 8, 2006