The Halo Assembly in Lambda-CDM: Observations in 7 Dimensions (HALO7D) dataset consists of Keck II/DEIMOS spectroscopy and Hubble Space Telescope-measured proper motions of Milky Way halo main sequence turnoff stars in the CANDELS fields. In this paper, we present the spectroscopic component of this dataset, and discuss target selection, observing strategy, and survey properties. We present a new method of measuring line-of-sight (LOS) velocities by combining multiple spectroscopic observations of a given star, utilizing Bayesian hierarchical modeling. We present the LOS velocity distributions of the four HALO7D fields, and estimate their means and dispersions. All of the LOS distributions are dominated by the hot halo: none of our fields are dominated by substructure that is kinematically cold in the LOS velocity component. Our estimates of the LOS velocity dispersions are consistent across the different fields, and these estimates are consistent with studies using other types of tracers. To complement our observations, we perform mock HALO7D surveys using the synthetic survey software Galaxia to observe the Bullock & Johnston (2005) accreted stellar halos. Based on these simulated datasets, the consistent LOS velocity distributions across the four HALO7D fields indicates that the HALO7D sample is dominated by stars from the same massive (or few relatively massive) accretion event(s).