We have searched for direct production of scalar top quarks at the Collider Detector at Fermilab in 88 pb-1 of p anti-p collisions at s**(1/2) = 1.8 TeV. We assume the scalar top quark decays into either a bottom quark and a chargino or a bottom quark, a lepton, and a scalar neutrino. The event signature for both decay scenarios is a lepton, missing transverse energy, and at least two b-quark jets. For a chargino mass of 90 GeV/c2 and scalar neutrino masses of at least 40 GeV/c2, we find no evidence for scalar top production and present upper limits on the production cross section in both decay scenarios.