  We have obtained deep, long-slit spectroscopy along the major axis of NGC
6166, the cD galaxy in the cluster Abell 2199, in order to measure the
kinematics of intracluster starlight at large radii. The velocity dispersion
rises beyond a few kpc, and steadily rises to 660 km/s at a radius of 60 kpc,
nearly reaching the velocity dispersion of the cluster (775+-50 km/s). These
data suggest that the stars in the halo of the cD trace the potential of the
cluster and that the kinematics of these intracluster stars can be used to
constrain the mass profile of the cluster. In addition, we find evidence for
systematic rotation in the intracluster stars beyond 20 kpc. The surface
brightness and velocity dispersion profiles can be fit using a single component
mass model only by making unphysical assumptions about the level of anisotropy
for both the stars in the cD galaxy and for the kinematics of the galaxies in
the cluster. Two-component mass models for the cD and its halo are explored
using the kinematics of known cluster members as an additional constraint
beyond the extent of the stellar kinematics. Assuming isotropy, the observed
kinematics can be reproduced only if the halo has a soft core, i.e., Alpha < 1
(Alpha=1 is excluded due to low implied stellar mass-to-light ratios). This
result is inconsistent with the predictions of current N-body simulations with
CDM. Assuming that our best-fit mass models for the Abell 2199 were placed at
cosmological redshifts between 0.2 <= z <= 0.5, the derived tangential critical
radii range from 5'' to 40'' consistent with the strong lensing observed in
intermediate redshift clusters. We also present Monte Carlo simulations that
test the reliability of velocity dispersions when the S/N is low.
