We predict a new type of steplike fluctuations in the magnetoconductan
ce of three-dimensional ballistic microwires. These mesoscopic fluctua
tions, which appear on a scale corresponding to a small fraction of th
e quantum unit of magnetic flux PHI0=hc/e, are a novel manifestation o
f the Aharonov-Bohm effect. The sharp conductance steps are caused by
the shift of electronic levels through the Fermi level in a magnetic f
ield. The flux-induced steps should be observable in, e.g., submicrome
ter Bi whiskers at temperatures of order 0.1 K. Sample-characteristic
fluctuations are predicted to appear in fields as low as a few gauss.