The Moon was probably formed by a catastrophic collision of the proto-Earth with a planetesimal named Theia. Most numerical models of this collision imply a higher portion of Theia in the Moon than in Earth. Because of the isotope heterogeneity among solar system bodies, the isotopic composition of Earth and the Moon should thus be distinct. So far, however, all attempts to identify the isotopic component of Theia in lunar rocks have failed. Our triple oxygen isotope data reveal a 12 +/- 3 parts per million difference in Delta O-17 between Earth and the Moon, which supports the giant impact hypothesis of Moon formation. We also show that enstatite chondrites and Earth have different Delta O-17 values, and we speculate on an enstatite chondrite-like composition of Theia. The observed small compositional difference could alternatively be explained by a carbonaceous chondrite-dominated late veneer.