We present measurements of Ortho-III phase correlations in an untwinned single crystal of YBa2Cu3O6.77 by neutron scattering and the novel method of hard (95 keV) X-ray scattering. The Ortho-III ordering is essentially two-dimensional, exhibiting Lorentzian peak shapes in the a-b plane. At room temperature, the correlation lengths deduced from the Lorentzian peak widths are about 5 unit cells (congruent-to 20 angstrom) along h and 19 unit cells (congruent-to 74 angstrom) along k, and are comparable to some correlation lengths measured for the Ortho-II phase. Upon heating, the superstructure intensity was found to decrease rapidly at temperatures above 50-degrees-C with about 10% of the original intensity remaining at 100-degrees-C and completely vanishing above 150-degrees-C. Such a low transition temperature explains why this phase is more difficult to observe than other superstructures, such as the Ortho-II.