  Tidal debris from infalling satellites can leave observable structure in the
phase-space distribution of the Galactic halo. Such substructure can be
manifest in the spatial and/or velocity distributions of the stars in the halo.
This paper focuses on a class of substructure that is purely kinematic in
nature, with no accompanying spatial features. To study its properties, we use
a simulated stellar halo created by dynamically populating the Via Lactea II
high-resolution N-body simulation with stars. A significant fraction of the
stars in the inner halo of Via Lactea share a common speed and metallicity,
despite the fact that they are spatially diffuse. We argue that this kinematic
substructure is a generic feature of tidal debris from older mergers and may
explain the detection of radial-velocity substructure in the inner halo made by
the Sloan Extension for Galactic Understanding and Exploration. The GAIA
satellite, which will provide the proper motions of an unprecedented number of
stars, should further characterize the kinematic substructure in the inner
halo. Our study of the Via Lactea simulation suggests that the stellar halo can
be used to map the speed distribution of the local dark-matter halo, which has
important consequences for dark-matter direct-detection experiments.
