We present a near-infrared spectroscopic study of HD 114762B , the latest-type metal-poor companion discovered to date and the only ultracool subdwarf with a known metallicity , inferred from the primary star to be [ Fe/H ] = –0.7 . We obtained a medium-resolution ( R \sim 3800 ) Keck/OSIRIS 1.18-1.40 \mu m spectrum and a low-resolution ( R \sim 150 ) IRTF/SpeX 0.8-2.4 \mu m spectrum of HD 114762B to test atmospheric and evolutionary models for the first time in this mass-metallicity regime . HD 114762B exhibits spectral features common to both late-type dwarfs and subdwarfs , and we assign it a spectral type of d/sdM9 \pm 1 . We use a Monte Carlo technique to fit PHOENIX/ GAIA synthetic spectra to the observations , accounting for the coarsely-gridded nature of the models . Fits to the entire OSIRIS J -band and to the metal-sensitive J -band atomic absorption features ( Fe i , K i , and Al i lines ) yield model parameters that are most consistent with the metallicity of the primary star and the high surface gravity expected of old late-type objects . The effective temperatures and radii inferred from the model atmosphere fitting broadly agree with those predicted by the evolutionary models of Chabrier & Baraffe , and the model color-absolute magnitude relations accurately predict the metallicity of HD 114762B . We conclude that current low-mass , mildly metal-poor atmospheric and evolutionary models are mutually consistent for spectral fits to medium-resolution J -band spectra of HD 114762B , but are inconsistent for fits to low-resolution near-infrared spectra of mild subdwarfs . Finally , we develop a technique for estimating distances to ultracool subdwarfs based on a single near-infrared spectrum . We show that this “ spectroscopic parallax ” method enables distance estimates accurate to \lesssim 10 % of parallactic distances for ultracool subdwarfs near the hydrogen burning minimum mass .