We have used the NICMOS NIC1 camera on the Hubble Space Telescope to obtain high-resolution near-infrared images of 27 nearby ultracool dwarfs with formal distance estimates less than 20 parsecs. One target, 2MASS J22551861-5713056, is resolved as a binary system, with a 4:1 flux ratio in the F110W passband. The primary has spectral type L6, and the revised spectroscopic parallax places it at a distance of ∼12 parsecs. The secondary is likely to have a spectral type between L8 and T1. The remaining 26 dwarfs are unresolved. Combining the present results with our earlier NICMOS (Near-Infrared Camera and Multi Object Spectrometer) observations and literature data, high-resolution imaging exists for 72 of the 85 L dwarfs in the current 20-parsec census. We derive a formal frequency of 15.3 +5.1 −3.3 % for resolved binaries in the local L-dwarf population. The frequency drops to 12.5 +5.3 −3.0 % if we take Malmquist bias into account. The NICMOS observations are capable of detecting systems with mass ratios q > 0.2, but all known binaries are near equal-mass, suggesting that low-q systems either fail to form, or have short lifetimes.