We present a measurement of the tt¯ production cross section using 194   pb−1 of CDF II data using events with a high transverse momentum electron or muon, three or more jets, and missing transverse energy. The measurement assumes 100% t→Wb branching fraction. Events consistent with tt decay are found by identifying jets containing heavy-flavor semileptonic decays to muons. The dominant backgrounds are evaluated directly from the data. Based on 20 candidate events and an expected background of 9.5±1.1 events, we measure a production cross section of 5.3±3.3+1.3−1.0   pb, in agreement with the standard model.