We search for standard model single-top-quark production in
the W-gluon fusion and W* channels using 106 pb-1 of data from p anti-p
collisions at s**(1/2) = 1.8 TeV collected with the Collider Detector
at Fermilab. We set an upper limit at 95% C.L. on the combined W-gluon
fusion and W* single-top cross section of 14 pb, roughly six times larger
than the standard model prediction. Separate 95% C.L. upper limits in
the W-gluon fusion and W* channels are also determined and are found to
be 13 and 18 pb, respectively.