We present analysis of Hubble Space Telescope (HST) planetary camera images of 20 L dwarfs identified in the course of the Two Micron All Sky Survey. Four of the targets, 2MASSW J0746425+200032, 2MASSs J0850359+105716, 2MASSW J0920122+351742, and 2MASSW J1146345+223053, have faint red companions at separations between 007 and 029 (1.6–7.6 AU). Ground-based infrared imaging confirms the last as a common proper motion companion. The surface density of background sources with comparable colors is extremely low, and we identify all four as physical binaries. In three cases, the bolometric magnitudes of the components differ by less than 0.3 mag. 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 mag fainter than the primary in the I band and ~0.8 mag fainter in M_bol. Indeed, 2M0850B is ~0.8 mag 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. We discuss the implications of these results for the temperature scale in the L/T transition region. 2M0850 is known to exhibit 6708 Å Li I absorption, indicating that the primary has a mass less than 0.06 M. Theoretical models predict that the magnitude difference implies a mass ratio of ≈0.75. The apparent binary fraction of the current sample, 20%, is comparable to the results of previous surveys of late-type M dwarfs in the field and in the Hyades. However, the mean separation of the L dwarf binaries in the current sample is smaller than the M dwarf value by a factor of 2, and only one system would be detected at the distance of the Hyades. We discuss the likely binary frequency among L dwarfs in light of these new data.