We present a kinetic calculation for the isotopic composition of stratospheric ozone. The calculated enrichments of 49O3 and 50O3 are in agreement with atmospheric measurements made at midlatitudes. Integrating the kinetic fractionation processes in the formation and photolysis of ozone, we obtain enrichments of ~7.5--10.5 and ~7.5--12.5% (referenced to atmospheric O2) for δ49O3 and δ50O3, respectively, at altitudes between 20 and 35 km; the photolysis in the Hartley band of ozone is responsible for the observed altitude variation. The overall magnitude of the ozone enrichments (~10%) is large compared with that commonly known in atmospheric chemistry and geochemistry. The heavy oxygen atom in ozone is therefore useful as a tracer of chemical species and pathways that involve ozone or its derived products. For example, the mass anomalies of oxygen in two greenhouse gases, CO2 and N2O, are likely the consequences of the transfer of heavy oxygen atoms from ozone.