We present the discovery of 2MASS J21321145+1341584AB as a closely separated ( 0.066 \arcsec ) 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 \pm 0.5 primary and an L7.5 \pm 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 \pm 0.3 AU ) 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 ( \sim 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 .