Using a numerical ray tracing code and a model of the suprathermal electron distribution in the inner magnetosphere, we calculate the Landau damping of chorus waves under realistic conditions. The chorus emissions are assumed to originate at the magnetic equatorial plane with a wave normal angle set at the generalized Gendrin angle, and a wave frequency which is varied from 0.1 to 0.9 of the equatorial electron gyrofrequency. Each ray is propagated until its wave power is diminished by a factor of 10, at which point we record the propagation time, latitude, and the distance along the ray path from the equator. Results indicate that chorus waves are expected to propagate to latitudes of 10¿--20¿ and are typically Landau damped before experiencing magnetospheric reflections, in agreement with satellite observations. In addition, we find longer propagation distances and lifetimes at those frequencies immediately above the half equatorial gyrofrequency and consider the possibility that this effect may contribute to the formation of the two-banded structure of chorus emissions.