The globular cluster ω Centauri is one of the largest and most massive members of the galactic system. However, its classification as a globular cluster has been challenged making it a candidate for being the stripped core of an accreted dwarf galaxy; this together with the fact that it has one of the largest velocity dispersions for star clusters in our galaxy makes it an interesting candidate for harboring an intermediate-mass black hole. We measure the surface brightness profile from integrated light on an HST ACS image of the center, and find a central power-law cusp of logarithmic slope -0.08. We also analyze Gemini GMOS-IFU kinematic data for a 5'' × 5'' field centered on the nucleus of the cluster, as well as for a field 14'' away. We detect a clear rise in the velocity dispersion from 18.6 km s-1 at 14'' to 23 km s-1 in the center. A rise in the velocity dispersion could be due to a central black hole, a central concentration of stellar remnants, or a central orbital structure that is radially biased. We discuss each of these possibilities. An isotropic, spherical dynamical model implies a black hole mass of 4.0-1.0+0.75 × 104 M☉, and excludes the no black hole case at greater than 99% significance. We have also run flattened, orbit-based models and find similar results. While our preferred model is the existence of a central black hole, detailed numerical simulations are required to confidently rule out the other possibilities.