We present the first parallax and luminosity measurements for an L subdwarf, the sdL7 2MASS J05325346+8246465. Observations conducted over 3 years by the USNO infrared astrometry program yield an astrometric distance of 26.7±1.2 pc and a proper motion of 2.6241"±0.0018"/yr. Combined with broadband spectral and photometric measurements, we determine a luminosity of logLbol/L☉=-4.24±0.06 and Teff=1730±90 K (the latter assuming an age of 5-10 Gyr), comparable to mid-type L field dwarfs. Comparison of the luminosity of 2MASS J05325346+8246465 to theoretical evolutionary models indicates that its mass is just below the sustained hydrogen-burning limit, and is therefore a brown dwarf. Its kinematics indicate a ∼110 Myr, retrograde Galactic orbit that is both eccentric (3 kpc≲R≲8.5 kpc) and extends well away from the plane (ΔZ=±2 kpc), consistent with membership in the inner halo population. The relatively bright J-band magnitude of 2MASS J05325346+8246465 implies significantly reduced opacity in the 1.2 µm region, consistent with inhibited condensate formation as previously proposed. Its as yet unknown subsolar metallicity remains the primary limitation in constraining its mass; determination of both parameters would provide a powerful test of interior and evolutionary models for low-mass stars and brown dwarfs.