The MACHO collaboration has recently analyzed 2.1 years of photometric data for about 8.5 million stars in the Large Magellanic Cloud (LMC). This analysis has revealed 8 candidate microlensing events and a total microlensing optical depth of $tau_{meas} = 2.9 +1.4/-0.9 times 10^{-7}$. This significantly exceeds the number of events (1.1) and the microlensing optical depth predicted from known stellar populations: $tau_{back} = 5.4times 10^{-8}$, but it is consistent with models in which about half of the standard dark halo mass is composed of Machos of mass $sim 0.5 msun$. One of these 8 events appears to be a binary lensing event with a caustic crossing that is partially resolved which allows us to estimate the distance to the lenses. If the source star is not a short period binary star, then we show that the lens system is very likely to reside in the LMC. However, if we assume that the optical depth for LMC-LMC lensing is large enough to account for our entire lensing signal, then the binary event does not appear to be consistent with lensing of a single LMC source star by a binary residing in the LMC. Thus, while the binary lens may indeed reside in the LMC, there is no indication that most of the lenses reside in the LMC.