The first detailed chemical abundance analysis of the M-dwarf (M4.0) exoplanet-hosting star Ross 128 is presented here, based upon near-infrared (1.5-1.7 mu m), high-resolution (R similar to 22,500) spectra from the SDSS Apache Point Galactic Evolution Experiment survey. We determined precise atmospheric parameters T-eff = 3231 +/- 100 K, log g = 4.96 +/- 0.11 dex and chemical abundances of eight elements (C, O, Mg, Al, K, Ca, Ti, and Fe), finding Ross 128 to have near solar metallicity ([Fe/H] = +0.03 +/- 0.09 dex). The derived results were obtained via spectral synthesis (1D LTE) adopting both MARCS and PHOENIX model atmospheres; stellar parameters and chemical abundances derived from the different adopted models do not show significant offsets. Mass-radius modeling of Ross 128b indicates that it lies below the pure-rock composition curve, suggesting that it contains a mixture of rock and iron, with the relative amounts of each set by the ratio of Fe/Mg. If Ross 128b formed with a subsolar Si abundance, and assuming the planet's composition matches that of the host star, it likely has a larger core size relative to the Earth despite this producing a planet with a Si/Mg abundance ratio similar to 34% greater than the Sun. The derived planetary parameters-insolation flux (S-Earth = 1.79 +/- 0.26) and equilibrium temperature (T-eq = 294. +/-. 10 K)-support previous findings that Ross 128b is a temperate exoplanet in the inner edge of the habitable zone.