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We present the lightcurves of 21 gravitational microlensing events from thefirst six years of the MACHO Project gravitational microlensing survey whichare likely examples of lensing by binary systems. These events were manuallyselected from a total sample of ~350 candidate microlensing events which wereeither detected by the MACHO Alert System or discovered through retrospectiveanalyses of the MACHO database. At least 14 of these 21 events exhibit strong(caustic) features, and 4 of the events are well fit with lensing by large massratio (brown dwarf or planetary) systems, although these fits are notnecessarily unique. The total binary event rate is roughly consistent withpredictions based upon our knowledge of the properties of binary stars, but aprecise comparison cannot be made without a determination of our binary lensevent detection efficiency.  Towards the Galactic bulge, we find a ratio of caustic crossing tonon-caustic crossing binary lensing events of 12:4, excluding one event forwhich we present 2 fits. This suggests significant incompleteness in ourability to detect and characterize non-caustic crossing binary lensing. Thedistribution of mass ratios, N(q), for these binary lenses appears relativelyflat. We are also able to reliably measure source-face crossing times in 4 ofthe bulge caustic crossing events, and recover from them a distribution of lensproper motions, masses, and distances consistent with a population of Galacticbulge lenses at a distance of 7 +/- 1 kpc. This analysis yields 2 systems withcompanions of ~0.05 M_sun.

Binary Microlensing Events from the MACHO Project