X-ray diffraction measurements of the sputter-annealed Si(111) 7×7 surface have been made at the National Synchrotron Light Source, Brookhaven. Technical advances have improved the reliability of such data significantly. The 120 structure factor intensities agree with the widely accepted structural model of Takayanagi at the 4σ level, but can be made to show complete agreement if the atomic coordinates of this model are allowed to relax. In this way, 15 of the 17 possible two-dimensional positional coordinates in three layers have been determined to an accuracy of ∼0.02 Å. The displacement pattern can be simply interpreted as a superposition of strain fields around the adatoms, in the dimers, and within the triangular island regions. These new observations of strain are discussed in the light of theoretical calculations of the local strain fields around adatoms, observations of reconstructed states of surfaces prepared under external strain, and theoretical attempts to understand the origin of strain.