We describe a search for anomalous production of events with two leptons (e or mu) of the same electric charge in pp[over ] collisions at a center-of-mass energy of 1.96 TeV. Many extensions to the standard model predict the production of two leptons of the same electric charge. This search has a significant increase in sensitivity compared to earlier searches. Using a data sample corresponding to 1 fb(-1) of integrated luminosity recorded by the CDF II detector, we observe no significant excess in an inclusive selection (expect 33.2+/-4.7 events, observe 44) or in a supersymmetry-optimized selection (expect 7.8+/-1.1 events, observe 13.).