  We show that the RMS fluctuation of the antisymmetric part of the Hall
conductance of a planar mesoscopic metal in a random magnetic field with zero
average is universal, of the order of $e^2/h$, independent of the amplitude of
the random magnetic field and the diffusion coefficient even in the weak field
limit. This quantity is exactly zero in the case of ordinary scalar disorder.
We propose an experiment to measure this surprising effect, and also discuss
its implications on the localization physics of this system. Our result applies
to some other systems with broken time-reversal ({\bf T}) symmetry.
