**EXHIBIT 31.1**
 
 **CERTIFICATION
        OF CHIEF EXECUTIVE OFFICER**
 **PURSUANT
        TO SECTION 302 OF**
 **THE
        SARBANES-OXLEY ACT OF 2002**
 
 I,
        Charles M. Baughn, certify that:
 
 1.
        I have
        reviewed this quarterly report on Form 10-Q of Hines Real Estate Investment
        Trust, Inc.;
 
 2. Based
        on my knowledge, this 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 report;
 
 3. Based
        on my knowledge, the financial statements, and other financial information
        included in this report, fairly present in all material respects the financial
        condition, results of operations and cash flows of the registrant as of,
        and
        for, the periods presented in this report;
 
 4. The
        registrant’s other certifying officer(s) 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 the registrant 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 the registrant, including its consolidated subsidiaries,
        is made known to us by others within those entities, particularly during
        the
        period in which this report is being prepared;
 
 b. evaluated
        the effectiveness of the registrant’s disclosure controls and procedures and
        presented in this report our conclusions about the effectiveness of the
        disclosure controls and procedures, as of the end of the period covered by
        this
        report based on such evaluation; and
 
 c. disclosed
        in this report any change in the registrant’s internal control over financial
        reporting that occurred during the registrant’s most recent fiscal quarter (the
        registrant’s fourth fiscal quarter in the case of an annual report) that has
        materially affected, or is reasonably likely to materially affect, the
        registrant’s internal control over financial reporting; and
 
 5. The
        registrant’s other certifying officer(s) and I have disclosed, based on our most
        recent evaluation of internal control over financial reporting, to the
        registrant’s auditors and the audit committee of the registrant’s board of
        directors (or persons performing the equivalent functions):
 
 a. all
        significant deficiencies and material weaknesses in the design or operation
        of
        internal control over financial reporting which are reasonably likely to
        adversely affect the registrant’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 the registrant’s internal control over financial
        reporting.
 
 
 Date:
        August 14,
        2007                                                                         /s/ CharlesM. Baughn
 Charles
        M. Baughn
 Chief
        Executive
        Officer