This paper presents the first results from a large spectroscopic survey of red giant branch ( RGB ) stars in M31 using DEIMOS on the Keck 10-meter telescope . A photometric pre-screening method , based on the intermediate-width DDO 51 band centered on the Mg b/MgH absorption feature , was used to select spectroscopic targets . RGB candidates were targeted in a small section of M31 ’ s giant southern tidal stream at a projected distance of 31 kpc from the galaxy ’ s center . We isolate a clean sample of 68 RGB stars by removing contaminants ( foreground Milky Way dwarf stars and background galaxies ) using a combination of spectroscopic , imaging , and photometric methods ; the surface-gravity-sensitive Na i doublet is particularly useful in this regard . About 65 % of the M31 stars are found to be members of the giant southern stream while the rest appear to be members of the general halo population . The mean ( heliocentric ) radial velocity of the stream in our field is -458 km s ^ { -1 } , blueshifted by -158 km s ^ { -1 } relative to M31 ’ s systemic velocity , in good agreement with recent velocity measurements at other points along the stream . The intrinsic velocity dispersion of the stream is found to be 15 _ { -15 } ^ { +8 } km s ^ { -1 } ( 90 % confidence limits ) . A companion paper by Font et al . ( 19 ) discusses possible orbits , implications of the coldness of the stream , and properties of the progenitor satellite galaxy . The kinematics , and possibly the metallicity distribution , of the general halo ( i.e. , non-stream ) population in this region of M31 indicate that it is significantly different from samples drawn from other parts of the M31 halo ; this is probably an indication of substructure in the halo . The stream appears to have a higher mean metallicity than the general halo : \langle [ Fe / H ] \rangle \sim - 0.54 versus -0.74 , and a smaller metallicity spread . The relatively high metallicity of the stream implies that its progenitor must have been a luminous dwarf galaxy . The Ca ii triplet line strengths of the M31 RGB stars are generally consistent with photometric estimates of their metallicity ( derived by fitting RGB fiducials in the color-magnitude diagram ) . There is indirect evidence of a population of intermediate-age stars in the stream .