Chaos and nonlinear dynamics of a bouncing proton in the presence of a kinetic Alfv¿n wave in the magnetosphere are studied. Particle motion is traced numerically in phase space using the Poincar¿ surface of section technique. With suitable initial conditions particle trajectories are calculated under paraxial approximation for several values of the wave amplitude. The trajectories show chaotic behavior at some finite amplitude of the wave. The threshold electrostatic field computed for the onset of chaos is less than the expected electric field associated with a kinetic Alfv¿n wave in the magnetosphere. This suggests that a kinetic Alfv¿n wave can lead to proton precipitation near the equatorial region.