We present analysis of HST Planetary Camera images of twenty L dwarfs identified in the course of the Two Micron All-Sky Survey. Four of the targets have faint, red companions at separations between 0.07 and 0.29 arcseconds (1.6 to 7.6 AU). In three cases, the bolometric magnitudes of the components differ by less than 0.3 magnitudes. Since the cooling rate for brown dwarfs is a strong function of mass, similarity in luminosities implies comparable masses. The faint component in the 2M0850 system, however, is over 1.3 magnitudes fainter than the primary in the I-band, and ~0.8 magnitudes fainter in M(bol). Indeed, 2M0850B is ~0.8 magnitudes fainter in I than the lowest luminosity L dwarf currently known, while the absolute magnitude we deduce at J is almost identical with M_J for Gl 229B. Theoretical models indicate a mass ratio of ~0.75. The mean separation of the L dwarf binaries in the current sample is smaller by a factor of two than amongst M dwarfs. We discuss the implications of these results for the temperature scale in the L/T transition region and for the binary frequency amongst L dwarfs.