We report the identification of 17 candidate brown dwarf binaries whose components straddle the L dwarf/T dwarf transition. These sources were culled from a large near-infrared spectral sample of L and T dwarfs observed with the Infrared Telescope Facility SpeX spectrograph. Candidates were selected on the basis of spectral ratios which segregate known (resolved) L dwarf/T dwarf pairs from presumably single sources. Composite templates, constructed by combining 13581 pairs of absolute flux-calibrated spectra, are shown to provide statistically superior fits to the spectra of our seventeen candidates as compared to single templates. Ten of these candidates appear to have secondary components that are significantly brighter than their primaries over the 1.0-1.3 micron band, indicative of rapid condensate depletion at the L dwarf/T dwarf transition. Our results support prior indications of enhanced multiplicity amongst early-type T dwarfs; 53+/-7% of the T0-T4 dwarfs in our spectral sample are found to be either resolved or unresolved (candidate) pairs, although this is consistent with an intrinsic (volume complete) brown dwarf binary fraction of only 15%. If verified, this sample of spectral binaries more than doubles the number of known L dwarf/T dwarf transition pairs, enabling a broader exploration of this poorly-understood phase of brown dwarf atmospheric evolution.