We present the discovery of 2MASS J21321145+1341584AB as a closely separated (0.066'') very low-mass field dwarf binary resolved in the near-infrared by the Keck II Telescope using laser guide star adaptive optics. Physical association is deduced from the angular proximity of the components and constraints on their common proper motion. We have obtained a near-infrared spectrum of the binary and find that it is best described by an L5{+-}0.5 primary and an L7.5{+-}0.5 secondary. Model-dependent masses predict that the two components straddle the hydrogen burning limit threshold with the primary likely stellar and the secondary likely substellar. The properties of this sytem - close projected separation (1.8{+-}0.3AU) and near unity mass ratio - are consistent with previous results for very low-mass field binaries. The relatively short estimated orbital period of this system ({approx}7-12 yr) makes it a good target for dynamical mass measurements. Interestingly, the system's angular separation is the tightest yet for any very low-mass binary published from a ground-based telescope and is the tightest binary discovered with laser guide star adaptive optics to date.