The structure of the (sqrt[5] x sqrt[5])R26.6 degrees reconstruction of LaAlO3 (001) has been determined using transmission electron diffraction combined with direct methods. It has a lanthanum oxide termination with one lanthanum vacancy per surface unit cell. Density functional calculations indicate that charge compensation occurs by a fractional number of highly delocalized holes, and that the surface contains no oxygen vacancies and the holes are not filled with hydrogen. The reconstruction can be understood in terms of expulsion of the more electropositive cation from the surface and increased covalency.