We present the results of a search for third generation leptoquark (LQ) pairs in 110±8pbࢤ1of p¯p collisions at √s=1.8TeV recorded by the Collider Detector at Fermilab. We assume third generation leptoquarks decay to a Τ lepton and a bquark with brancing ratio β. We observe one candidate event, consistent with standard model background expectations. We place upper limits on σ(p¯p→LQLQ¯)β2 as a function of the leptoquark mass MLQ. We exclude at 95% confidence level scalar leptoquarks with MLQ<99GeV/c2, gauge vector leptoquarks with MLQ<225GeV/c2, and nongauge vector leptoquarks with MLQ<170GeV/c2 for β=1.