Although many models have been proposed, the physical mechanisms responsible for the formation of low-mass brown dwarfs (BDs) are poorly understood. The multiplicity properties and minimum mass of the BD mass function provide critical empirical diagnostics of these mechanisms. We present the discovery via gravitational microlensing of two very low mass, very tight binary systems. These binaries have directly and precisely measured total system masses of 0.025 M ☉ and 0.034 M ☉, and projected separations of 0.31 AU and 0.19 AU, making them the lowest-mass and tightest field BD binaries known. The discovery of a population of such binaries indicates that BD binaries can robustly form at least down to masses of ~0.02 M ☉. Future microlensing surveys will measure a mass-selected sample of BD binary systems, which can then be directly compared to similar samples of stellar binaries.