We report a search for the production of long-lived charged massive particles in a data sample of 90   pb−1 of s√=1.8   TeV pp¯ collisions recorded by the Collider Detector at Fermilab. The search uses the muonlike penetration and anomalously high ionization energy loss signature expected for such a particle to discriminate it from backgrounds. The data are 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.