We present a new analysis of the transport of cosmic rays in a turbulent magnetic field that varies in all three spatial dimensions. The analysis utilizes a numerical simulation that integrates the trajectories of an ensemble of test particles from which we obtain diffusion coefficients based on the particle motions. We find that the diffusion coefficient parallel to the mean magnetic field is consistent with values deduced from quasi-linear theory, in agreement with earlier work. The more interesting and less understood transport perpendicular to the average magnetic field is found to be enhanced (above the classical scattering result) by the random walk, or braiding, of the magnetic field. The value of κ⊥ obtained is generally larger than the classical scattering value but smaller than the quasi-linear value. The computed values of κ⊥/κ∥, for a representation of the interplanetary magnetic field, are 0.02–0.04; these values are of the same general magnitude as those assumed in recent numerical simulations of cosmic-ray modulation and transport in the heliosphere, and give reasonable agreement with spacecraft observations of cosmic rays. Some consequences of these results for the interpretation of heliospheric observations are discussed.