  We describe a search for a third generation vector leptoquark (VLQ3) that
decays to a b quark and tau lepton using the CDF II detector and 322 pb^(-1) of
integrated luminosity from the Fermilab Tevatron. Vector leptoquarks have been
proposed in many extensions of the standard model (SM). Observing a number of
events in agreement with SM expectations, assuming Yang-Mills (minimal)
couplings, we obtain the most stringent upper limit on the VLQ3 pair production
cross section of 344 fb (493 fb) and lower limit on the VLQ3 mass of 317
GeV/c^2 (251 GeV/c^2) at 95% C.L.
