As part of the SPLASH survey of the Andromeda (M31) system, we have obtained Keck/DEIMOS spectra of the compact elliptical (cE) satellite M32. This is the first resolved-star kinematical study of any cE galaxy. In contrast to most previous kinematical studies that extended out to r≾30" ~ 1 r^(eff) I ~ 100 pc, we measure the rotation curve and velocity dispersion profile out to r ~ 250" and higher order Gauss-Hermite moments out to r ~ 70". We achieve this by combining integrated-light spectroscopy at small radii (where crowding/blending are severe) with resolved stellar spectroscopy at larger radii, using spatial and kinematical information to account statistically for M31 contamination. The rotation curve and velocity dispersion profile extend well beyond the radius (r ~ 150") where the isophotes are distorted. Unlike NGC 205, another close dwarf companion of M31, M32's kinematics appear regular and symmetric and do not show obvious sharp gradients across the region of isophotal elongation and twists. We interpret M31's kinematics using three-integral axisymmetric dynamical equilibrium models constructed using Schwarzschild's orbit superposition technique. Models with a constant mass-to-light ratio can fit the data remarkably well. However, since such a model requires an increasing tangential anisotropy with radius, invoking the presence of an extended dark halo may be more plausible. Such an extended dark halo is definitely required to bind a half-dozen fast-moving stars observed at the largest radii, but these stars may not be an equilibrium component of M32
