We report on a search for anomalous production of events with at least two charged, isolated, like-sign leptons, each with pT>11  GeV/c using a 107  pb−1 sample of 1.8 TeV pp¯ collisions collected by the CDF detector. We define a signal region containing low background from standard model processes. To avoid bias, we fix the final cuts before examining the event yield in the signal region using control regions to test the Monte Carlo predictions. We observe no events in the signal region, consistent with an expectation of 0.63+0.84−0.07 events. We present 95% confidence level limits on new physics processes in both a signature-based context as well as within a representative minimal supergravity (tanβ=3) model.