The dynamical system composed of a charged particle moving in a two-dimensional magnetic field containing a neutral point, with and without a perpendicular electric field, is studied. The system is found to be nonintegrable and chaotic. Lyapunov characteristic exponents are calculated for the various types of chaotic orbits. When parameters relevant to the magetotail are used it is found that the stochastic nature of the motion is more important for a thick current sheet (20,000 km) than for a thin sheet (1000 km). Some consequences of this stochasticity are discussed, including the suggestion of a collisionless, ''chaotic conductivity'': this represents the collisionlike randomizing effect of the chaotic dynamics.