I present a new analysis of the MACHO Project 5.7 yr Large Magellanic Cloud (LMC) microlensing data set that incorporates the effects of contamination of the microlensing event sample by variable stars. Photometric monitoring of MACHO LMC microlensing event candidates by the EROS and OGLE groups has revealed that one of these events is likely to be a variable star, while additional data have confirmed that many of the other events are very likely to be microlensing. These additional data on the nature of the MACHO microlensing candidates are incorporated into a simple likelihood analysis to derive a probability distribution for the number of MACHO microlens candidates that are true microlensing events. This analysis shows that 10-12 of the 13 events that passed the MACHO selection criteria are likely to be microlensing events, with the other 1-3 being variable stars. This likelihood analysis is also used to show that the main conclusions of the MACHO LMC analysis are unchanged by the variable star contamination. The microlensing optical depth toward the LMC is τ=1.0±0.3x10–7. If this is due to microlensing by known stellar populations plus an additional population of lens objects in the Galactic halo, then the new halo population would account for 16% of the mass of a standard Galactic halo. The MACHO detection exceeds the expected background of two events expected from ordinary stars in standard models of the Milky Way and LMC at the 99.98% confidence level. The background prediction is increased to three events if maximal disk models are assumed for both the Milky Way and LMC, but this model fails to account for the full signal seen by MACHO at the 99.8% confidence level.