**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:
      November 14,
      2007                                                                                     /s/ CHARLESM. BAUGHN


Charles
      M. Baughn


Chief
      Executive Officer