Tropospheric 18O18O is an emerging proxy for past tropospheric ozone and free-tropospheric temperatures. The basis of these applications is the idea that isotope-exchange reactions in the atmosphere drive 18O18O abundances toward isotopic equilibrium. However, previous work used an offline box-model framework to explain the 18O18O budget, approximating the interplay of atmospheric chemistry and transport. This approach, while convenient, has poorly characterized uncertainties. To investigate these uncertainties, and to broaden the applicability of the 18O18O proxy, we developed a scheme to simulate atmospheric 18O18O abundances (quantified as ∆36 values) online within the GEOS-Chem chemical transport model. These results are compared to both new and previously published atmospheric observations from the surface to 33 km. Simulations using a simplified O2 isotopic equilibration scheme within GEOS-Chem show quantitative agreement with measurements only in the middle stratosphere; modeled ∆36 values are too high elsewhere. Investigations using a comprehensive model of the O-O2-O3 isotopic photochemical system and proof-of-principle experiments suggest that the simple equilibration scheme omits an important pressure dependence to ∆36 values: the anomalously efficient titration of 18O18O to form ozone. Incorporating these effects into the online ∆36 calculation scheme in GEOS-Chem yields quantitative agreement for all available observations. While this previously unidentified bias affects the atmospheric budget of 18O18O in O2, the modeled change in the mean tropospheric ∆36 value since 1850 C.E. is only slightly altered; it is still quantitatively consistent with the ice-core ∆36 record, implying that the tropospheric ozone burden increased less than ~40% over the twentieth century.