We demonstrate that the nonlinear I-V characteristics of a two-probe conductor are not an even function of a magnetic field. While the conductance of a two-probe conductor is even in a magnetic field, we find that alreadythe contributions to the current that are second order in voltage, are in general not even. This implies a departure from the Onsager microreversibility principle in the weakly nonlinear regime. Interestingly, the effect that we find is due to the Coulomb interaction. A measurement of magnetic-field asymmetry can be used to determine the effective interaction strength. As a generic example, we discuss the I-V characteristics of a chaotic quantum dot. The ensemble averaged I-V of such a cavity is linear: nonlinearities are due to quantum interference. Consequently, phase-breaking reduces the asymmetry. We support this statement with a calculation that treats inelastic scattering with the help of a voltage probe.