Oxygen isotope measurements of carbonate from martian meteorite ALH 84001 (delta(18)O = 18.3 +/- 0.4 per mil, delta(17)O = 10.3 +/- 0.2 per mil, and Delta(17)O = 0.8 +/- 0.05 per mil) are fractionated with respect to those of silicate minerals. These measurements support the existence of two oxygen isotope reservoirs (the atmosphere and the silicate planet) on Mars at the time of carbonate growth. The cause of the atmospheric oxygen isotope anomaly may be exchange between CO2 and O(D-1) produced by the photodecomposition of ozone. Atmospheric oxygen isotope compositions may be transferred to carbonate minerals by CO2-H2O exchange and mineral growth. A sink of O-17-depleted oxygen, as required by mass balance, may exist in the planetary regolith.