We present spectroscopic observations with the Keck Low-Resolution Imaging Spectrometer of LBQS 0015+0239, a pair of quasars at z=2.45 with a separation of Δθ=2".2 (projected linear distance of 17.8 h–170 kpc, for Ωm=0.3, Λ=0.7). Lensing is an unlikely interpretation for the images since the spectra show significant differences in the N V and C IV emission-line profiles and there is no luminous galaxy at the anticipated lens position. Rather, we interpret this pair as the highest redshift known example of a binary quasar. The redshift difference of 661±173 km.s–1 between the two components is inconsistent with the lensing expectation but is consistent with the line-of-sight velocity difference of a bound pair of galaxies. The spectra show associated narrow metal absorption in highly ionized species of C and N, with a systemic velocity difference of 492±6 km.s–1. It is likely that this absorption arises in a group or cluster of galaxies surrounding the quasar pair. After a thorough search, the Large Bright Quasar Survey is known to contain one gravitational lens and four probable binary pairs. The existence of close binaries is evidence that quasar activity can be triggered by galaxy interactions. We speculate that the close pair LBQS 0015+0239 is a rare example of the premerger state of two supermassive black holes.