Red optical and near-infrared spectroscopy are presented for SDSS J125637.13-022452.4, one of only four L subdwarfs reported to date. These data confirm the low-temperature, metal-poor nature of this source, as indicated by prominent metal-hydride bands, alkali lines, and collision-induced H₂ absorption. The optical and near-infrared spectra of SDSS J1256-0224 are similar to those of the sdL4 2MASS J16262034+3925190, and we derive a classification of sdL3.5 based on the preliminary scheme of Burgasser, Cruz, and Kirkpatrick. The kinematics of SDSS J1256-0224 are consistent with membership in the Galactic inner halo, with estimated UVW space velocities indicating a slightly prograde, eccentric, and inclined Galactic orbit (3.5 R 11 kpc; Z _max = 7.5 kpc). Comparison to synthetic spectra computed with the PHOENIX code, including the recent implementation of kinetic condensate formation (DRIFT-PHOENIX), indicates T _eff 2100-2500 K and [M/H] –1.5 to –1.0 for log g 5.0-5.5 (cgs), although there are clear discrepancies between model and observed spectra particularly in the red optical region. As such, any conclusions on the role of metallicity in condensate grain and cloud formation are probably premature. Indeed, a shift in the temperature scale of L subdwarfs relative to L dwarfs may obviate the need for modified condensate and grain chemistry in low metallicity atmospheres.