We report discovery of a young 0.32 L dwarf binary, SDSS J2249+0044AB, found as the result of a Keck LGSAO imaging survey of young field brown dwarfs. Weak K, Na, and FeH features as well as strong VO absorption in the integrated-light J-band spectrum indicate a young age for the system. From spatially resolved K-band spectra we determine spectral types of L3 and L5 for components A and B, respectively. SDSS J2249+0044A is spectrally very similar to G196-3B, an L3 companion to a young M2.5 field dwarf. Thus, we adopt 100 Myr (the age estimate of the G196-3 system) as the age of SDSS J2249+0044AB, but ages of 12-790 Myr are possible. By comparison to G196-3B, we estimate a distance to SDSS J2249+0044AB of 54 +- 16 pc and infer a projected separation of 17 +- 5 AU for the binary. Comparison of the luminosities to evolutionary models at an age of 100 Myr yields masses of 0.029 and 0.022 Msun for SDSS J2249+0044A and B, respectively. Over the possible ages of the system (12-790 Myr), the mass of SDSS J2249+0044A could range from 0.011 to 0.070 Msun and the mass of SDSS J2249+0044B could range from 0.009 to 0.065 Msun. Evolutionary models predict that either component could be burning deuterium, which could result in a mass ratio as low as 0.4, or alternatively, a reversal in the luminosities of the binary. We find a likely proper motion companion, GSC 00568-01752, which lies 48.9 away (2600 AU) and has SDSS+2MASS colors consistent with an early M dwarf. The photometric distance to GSC 00568-01752 is 53 +- 15 pc, in agreement with our distance estimate for SDSS J2249+0044AB. The space motion of SDSS J2249+0044AB shows no obvious coincidence with known young moving groups. The unusually red near-IR colors, young age, and low masses of the binary make it an important template for studying planetary-mass objects found by direct imaging surveys.
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