During the Galileo flybys of Callisto in 1999, a CO2 atmosphere and an ionosphere were detected. Using the Caltech/Jet Propulsion Laboratory one-dimensional KINETICS model, we have successfully simulated the observed electron density within a factor of 2, while satisfying the observational constraints on carbon and oxygen atoms. We conclude that photoionization of CO2 alone is insufficient to produce the observed electron density. An atmosphere 20--100 times denser than the CO2 atmosphere must be introduced, as suggested by Kliore et al. (2002). We show that an O2-rich atmosphere is highly probable. However, the atomic oxygen produced from O2 photodissociation is 2 orders of magnitude greater than the upper limit given by Strobel et al. (2002). The introduction of reactive hydrogen chemistry assuming a surface abundance of H2O of ~2 ¿ 109 cm-3 (4 ¿ 10-8 mbar) is required to reduce the excess atomic O abundance. The calculated atomic O column density is >5 ¿ 1012 cm-2, which is about the observed upper limit, suggesting we should be able to detect O in the atmosphere of Callisto.