We present spectroscopic observations of red giant branch (RGB) stars in the Andromeda spiral galaxy (M31), acquired with the DEIMOS instrument on the Keck II 10-m telescope. The three fields targeted in this study are in the M31 spheroid, outer disk, and giant southern stream. In this paper, we focus on the kinematics and chemical composition of RGB stars in the stream field located at a projected distance of R = 20 kpc from M31s center. A mix of stellar populations is found in this field. M31 RGB stars are isolated from Milky Way dwarf star contaminants using a variety of spectral and photometric diagnostics. The radial velocity distribution of RGB stars displays a clear bimodality -- a primary peak centered at v = -513 km/s and a secondary one at v = -417 km/s -- along with an underlying broad component that is presumably representative of the smooth spheroid of M31. Both peaks are found to be dynamically cold with intrinsic velocity dispersions of sigma(v) = 16 km/s. The mean metallicity and metallicity dispersion of stars in the two peaks is also found to be similar: [Fe/H] = -0.45 and sigma([Fe/H]) = 0.2. The observed velocity of the primary peak is consistent with that predicted by dynamical models for the stream, but there is no obvious explanation for the secondary peak. The nature of the secondary cold population is unclear: it may represent: (1) tidal debris from a satellite merger event that is superimposed on, but unrelated to, the giant southern stream; (2) a wrapped around component of the giant southern stream; (3) a warp or overdensity in M31s disk at R > 50 kpc (this component is well above the outward extrapolation of the smooth exponential disk brightness profile).
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