We present a search for the flavor-changing neutral current decays
B^0_d -> mu^+mu^- and B^0_s -> mu^+mu^- in ppbar collisions at sqrt s = 1.8
TeV, using 98 pb^-1 of data collected at the Collider Detector at Fermilab.
We find one candidate event for these decays, which is consistent with the
background estimates, and set upper limits on the branching fractions of
B(B^0_d -> mu^+mu^-)<8.6 x 10^-7 and B(B^0_s -> mu^+mu^-)<2.6 x 10^-6 at 95%
confidence level.