The diffusion of fast electrons in a stochastic magnetic field is considered for the simple case of the fluctuating field parallel to the steady field. The assumption defining the fast electrons is that their particle velocity is greater than the phase velocity characteristic of the fluctuating field. In the limit of observation times greater than both the Larmor period and the correlation time of the stochastic field, the diffusion coefficient can be obtained explicitly as a function of the ratio of the correlation time to the Larmor period and the result holds for all values of the ratio of these characteristic times. The result and hence the assumptions in the derivation are checked by Monte Carlo calculations.