  We report the discovery of an L-type companion to the young M3.5V star 2MASS
J01225093-2439505 at a projected separation of 1.45" (~52 AU) as part of our
adaptive optics imaging search for extrasolar giant planets around young
low-mass stars. 2MASS 0122-2439 B has very red near-infrared colors similar to
the HR 8799 planets and the reddest known young/dusty L dwarfs in the field.
Moderate-resolution (R~3800) 1.5-2.4 $\mu$m spectroscopy reveals a
near-infrared spectral type of L4-L6 and an angular H-band shape, confirming
its cool temperature and young age. The kinematics of 2MASS 0122-2439 AB are
marginally consistent with members of the ~120 Myr AB Dor young moving group
based on the photometric distance to the primary (36 +/- 4 pc) and our radial
velocity measurement of 2MASS 0122-2439 A from Keck/HIRES. We adopt the AB Dor
group age for the system, but the high energy emission, lack of Li I
$\lambda$6707 absorption, and spectral shape of 2MASS 0122-2439 B suggest a
range of ~10-120 Myr is possible. The age and luminosity of 2MASS 0122-2439 B
fall in a strip where "hot-start" evolutionary model mass tracks overlap as a
result of deuterium burning. The implied mass of 2MASS 0122-2439 B is ~12-13
Mjup or ~22-27 Mjup if it is an AB Dor member, or possibly as low as 11 Mjup if
the wider age range is adopted. Evolutionary models predict an effective
temperature for 2MASS 0122-2439 B that corresponds to spectral types near the
L/T transition (~1300-1500 K) for field objects. However, we find a mid-L
near-infrared spectral type, indicating that 2MASS 0122-2439 B represents
another case of photospheric dust being retained to cooler temperatures at low
surface gravities, as seen in the spectra of young (8-30 Myr) planetary
companions. [Abridged]
