The possible enhancement of isotropically heavy ozone (50O3) in the earth's stratosphere and mesosphere produced by the preferential photodissociation of heavy oxygen (34O2) is considered. On the basis of a realistic oxygen-only model, we show that the rapidity of the exchange reaction 18O+32O2⇄16O+34O2 prevents any enhancement of stratospheric temperatures. Since observations of Mauersberger (1981) suggest that such an enhancement exists, one is left with a paradox. Possible modifications to the chemical model, which include isotopically isotopically specific photochemistry of ozone, are shown to be non-competitive with the exchange reaction.