We present the results of a search for third generation leptoquark
(LQ) pairs in 110 +/- 8 pb^-1 of pbar p collisions at sqrt s = 1.8 TeV
recorded by the Collider Detector at Fermilab.  We assume third generation
leptoquarks decay to a tau lepton and a b quark with branching ratio Beta.  We
observe one candidate event, consistent with standard model background
expectations.  We place upper limits on sigma(pbar p -> LQ \overbar LQ) - Beta
^2 as a function of the leptoquark mass M_LQ.  We exclude at 95% confidence
level scalar leptoquarks with M_LQ < 99 GeV/c^2, gauge vector leptoquarks with
M_LQ < 225 GeV/c^2, and nongauge vector leptoquarks with M_LQ < 170 GeV/c^2
for Beta = 1.