We investigate theoretically the effect of a finite electric field on the resistivity of a disordered one-dimensional system in the variable-range hopping regime. We find that at low fields the transport is inhibited by rare fluctuations in the random distribution of localized states that create high-resistance breaks in the hopping network. As the field increases, the breaks become less resistive. In strong fields the breaks are overrun and the electron distribution function is driven far from equilibrium. The logarithm of the resistance initially shows a simple exponential drop with the field, followed by a logarithmic dependence, and finally, by an inverse square-root law.