We report the first results of a program to study the internal kinematics of globular clusters in the outer halo of the Milky Way. Using the Keck telescope and High Resolution Echelle Spectrometer, we have measured precise radial velocities for 30 candidate red giants in the direction of Palomar 13, an object traditionally cataloged as a compact, low-luminosity globular cluster. We have combined these radial velocities with published proper motion membership probabilities and new CCD photometry from the Keck and Canada-France-Hawaii telescopes to isolate a sample of 21 probable members. We find a systemic velocity of &angl0; v r &angr0; s= 24.1�0.5 km s-1 and a projected, intrinsic velocity dispersion of σ p= 2.2�0.4 km s-1. Although modest, this dispersion is nevertheless several times larger than that expected for a globular cluster of this luminosity and central concentration. Taken at face value, it implies a mass-to-light ratio of ϒ V= 40 based on the best-fit King-Michie model. The surface density profile of Palomar 13 also appears unusual compared to most Galactic globular clusters; depending upon the details of background subtraction and model-fitting, Palomar 13 either contains a substantial population of" extratidal" stars, or is considerably more spatially extended than previously suspected. The full surface density profile is equally well fitted by a King-Michie model having a high concentration and large tidal radius, or by a Navarro-Frenk-White model. We examine—and tentatively reject—a number of possible origins for the observed characteristics of Palomar 13 (eg, velocity" jitter" among the red giant branch stars, spectroscopic binary stars, nonstandard mass functions, modified Newtonian dynamics) and conclude that the two leading explanations are either catastrophic heating during a recent perigalacticon passage or the presence of a dark matter halo. The available evidence therefore suggests that Palomar 13 is either a globular cluster that is now in the process of dissolving into the Galactic halo or a faint, dark matter–dominated stellar system.