The Earth-Moon system likely formed as a result of a collision between two large planetary objects. Debate about their relative masses, the impact energy involved, and the extent of isotopic homogenization continues. We present the results of a high-precision oxygen isotope study of an extensive suite of lunar and terrestrial samples. We demonstrate that lunar rocks and terrestrial basalts show a 3 to 4 ppm (parts per million), statistically resolvable, difference in Delta O-17. Taking aubrite meteorites as a candidate impactor material, we show that the giant impact scenario involved nearly complete mixing between the target and impactor. Alternatively, the degree of similarity between the Delta O-17 values of the impactor and the proto-Earth must have been significantly closer than that between Earth and aubrites. If the Earth-Moon system evolved from an initially highly vaporized and isotopically homogenized state, as indicated by recent dynamical models, then the terrestrial basalt-lunar oxygen isotope difference detected by our study may be a reflection of post-giant impact additions to Earth. On the basis of this assumption, our data indicate that post-giant impact additions to Earth could have contributed between 5 and 30% of Earth's water, depending on global water estimates. Consequently, our data indicate that the bulk of Earth's water was accreted before the giant impact and not later, as often proposed.