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 , 2MASSW J0746425+200032 , 2MASSs J0850359+105716 , 2MASSW J0920122+351742 and 2MASSW J1146345+223053 , have faint , red companions at separations between 0.07 and 0.29 arcseconds ( 1.6 to 7.6 AU ) . Ground-based infrared imaging confirms the last as a common proper-motion companion . The surface density of background sources with comparable colours 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 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 \sim 0.8 magnitudes fainter in M _ { bol } . Indeed , 2M0850B is \sim 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 . We discuss the implications of these results for the temperature scale in the L/T transition region . 2M0850 is known to exhibit \lambda 6708 Å Li I absorption , indicating that the primary has a mass less than 0.06M _ { \odot } . Theoretical models predict that the magnitude difference implies a mass ratio of \approx 0.75 . The apparent binary fraction of the current sample , 20 % , is comparable with the results of previous surveys of late-type M dwarfs in the field and in the Hyades cluster . However , the mean separation of the L dwarf binaries in the current sample is smaller by a factor of two than the M dwarf value , and only one system would be detected at the distance of the Hyades . We discuss the likely binary frequency amongst L dwarfs in light of these new data .