We report a search for production of long-lived charged massive
particles in a data sample of 90 pb-1 of s**(1/2) = 1.8 TeV p anti-p collisions
recorded by the Collider Detector at Fermilab (CDF). The search uses the
muon-like penetration and anomalously high ionization energy loss signature
expected for such a particle to discriminate it from backgrounds. The data
is found to agree with background expectations, and cross section limits of
O(1) pb are derived using two reference models, a stable quark and a stable
scalar lepton.