We present 947 radial velocities of RR Lyrae variable stars in four fields located toward the Galactic bulge, observed within the data from the ongoing Bulge RR Lyrae Radial Velocity Assay (BRAVA-RR). We show that these RR Lyrae stars (RRLs) exhibit hot kinematics and null or negligible rotation and are therefore members of a separate population from the bar/pseudobulge that currently dominates the mass and luminosity of the inner Galaxy. Our RRLs predate these structures. and have metallicities, kinematics, and spatial distribution that are consistent with a "classical" bulge, although we cannot yet completely rule out the possibility that they are the metal-poor tail of a more metal-rich ([Fe/H] similar to -1 dex) halo-bulge population. The complete catalog of radial velocities for the BRAVA-RR stars is also published electronically.