The isotopic composition of long-lived trace molecules provides a window into atmospheric transport and chemistry. Carbon dioxide is a particularly powerful tracer, because its abundance remains >100 parts per million by volume (ppmv) in the mesosphere. Here, we successfully reproduce the isotopic composition of CO(2) in the middle atmosphere, which has not been previously reported. The mass-independent fractionation of oxygen in CO(2) can be satisfactorily explained by the exchange reaction with O((1)D). In the stratosphere, the major source of O((1)D) is O(3) photolysis. Higher in the mesosphere, we discover that the photolysis of (16)O(17)O and (16)O(18)O by solar Lyman-alpha radiation yields O((1)D) 10-100 times more enriched in (17)O and (18)O than that from ozone photodissociation at lower altitudes. This latter source of heavy O((1)D) has not been considered in atmospheric simulations, yet it may potentially affect the "anomalous" oxygen signature in tropospheric CO(2) that should reflect the gross carbon fluxes between the atmosphere and terrestrial biosphere. Additional laboratory and atmospheric measurements are therefore proposed to test our model and validate the use of CO(2) isotopic fractionation as a tracer of atmospheric chemical and dynamical processes.