We present a catalog of high-precision proper motions in the Orion Nebula Cluster (ONC), based on Treasury Program observations with the Hubble Space Telescope's (HST) ACS/WFC camera. Our catalog contains 2454 objects in the magnitude range of 14.2 < mF775W < 24.7, thus probing the stellar masses of the ONC from ∼0.4 M☉ down to ∼0.02 M☉ over an area of ∼550 arcmin2. We provide a number of internal velocity dispersion estimates for the ONC that indicate a weak dependence on stellar location and mass. There is good agreement with the published velocity dispersion estimates, although nearly all of them (including ours at and mas yr−1) might be biased by the overlapping young stellar populations of Orion A. We identified four new ONC candidate runaways based on HST and the Gaia DR 2 data, all with masses less than ∼1 M☉. The total census of known candidate runaway sources is 10-one of the largest samples ever found in any Milky Way open star cluster. Surprisingly, none of them have tangential velocities exceeding 20 km s−1. If most of them indeed originated in the ONC, it may compel the re-examination of dynamical processes in very young star clusters. It appears that the mass function of the ONC is not significantly affected by the lost runaways.