  We calculate the rate of production of W+Upsilon and Z+Upsilon at the
Tevatron. We find the cross sections at a center-of-mass energy of 1.8 TeV to
be roughly 450 pb for W+Upsilon and 150 pb for Z+Upsilon. The dominant
production mechanism involves the binding of a color-octet b-bbar pair into a
P-wave bottomonium state which subsequently decays into Upsilon. The purely
leptonic decay modes of Upsilon, W, and Z provide signatures with small
backgrounds. In Run I of the Tevatron, the number of events in the purely
leptonic decay channels before allowing for detector acceptances and
efficiencies should be about 500 for W+Upsilon and about 60 for Z+Upsilon. We
conclude that W+Upsilon events may be observable in the Run I data.
