A model of the hot oxygen geocorona in the transition region near the exobase is described. It is based on a Monte Carlo solution of the nonlinear Boltzmann equation for hot oxygen atoms produced by chemical processes usually considered as a source of hot oxygen (photodissociation of O2 and dissociative recombination of O2+ and NO+ ions). The evolution of the system is described stochastically as a series of random Markovian processes. The energy distribution function of the thermal and non-thermal O(³P) atoms and of the nonthermal O(¹D) atoms is calculated from the thermospheric collision-dominated region to the exosphere where the gas flow is virtually collisionless. The model is applied to equatorial latitudes for conditions of low solar and geomagnetic activity. Numerical simulations show that the distribution function of thermal oxygen is increasingly perturbed by collisions with the hot oxygen population at high altitudes and departs significantly from a Maxwellian distribution at all altitudes. The number density and temperature of the nonthermal oxygen atoms are derived from their microscopic distribution function and found to be in qualitative agreement with previous theoretical and experimental estimates.