We present IRTF SpeX observations of the M/L binary system 2MASS J17072343-0558249. SpeX imaging resolves the system into a 1"01+/-0.17 visual binary in which both components have red near infrared colors. Resolved low-resolution (R~150) 0.8-2.5 micron spectroscopy reveals strong H2O, CO and FeH bands and alkali lines in the spectra of both components, characteristic of late-type M and L dwarfs. A comparison to a sample of late-type field dwarf spectra indicates spectral types M9 and L3. Despite the small proper motion of the system (0"100+/-0"009 yr^{-1}), imaging observations over 2.5 yr provide strong evidence that the two components share common proper motion. Physical association is also likely due to the small spatial volume occupied by the two components (based on spectrophotometric distances estimates of 15+/-1 pc) as compared to the relatively low spatial density of low mass field stars. The projected separation of the system is 15+/-3 AU, similar to other late-type M and L binaries. Assuming a system age of 0.5-5 Gyr, we estimate the masses of the binary components to be 0.072-0.083 and 0.064-0.077 M_sun, with an orbital period of roughly 150-300 yr. While this is nominally too long a baseline for astrometric mass measurements, the proximity and relatively wide angular separation of the 2MASS J1707-0558AB pair makes it an ideal system for studying the M dwarf/L dwarf transition at a fixed age and metallicity.