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We analyze data from the Hubble Space Telescope's Advanced Camera for Surveysof the globular cluster Omega Cen. We construct a photometric and proper-motioncatalog using the GO-9442, GO-10252, and GO-10775 data sets. The 2.5- to 4-yearbaseline between observations yields a catalog of some 10^5 proper motions,with 53,382 high-quality measurements in a central field. We determine thecluster center to ~1-arcsecond accuracy using two different star-count methods,and a completely independent method using 2MASS images. We also determine thekinematical center of the proper motions, which agrees with the star-countcenter to within its uncertainty. The proper-motion dispersion of the clusterincreases gradually inwards, but there is no variation in kinematics withposition within the central ~15 arcsec: there is no dispersion cusp and nostars with unusually high velocities. We measure for the first time in anyglobular cluster the variation in proper-motion dispersion with mass along themain sequence, and find the cluster not yet to be in equipartition. Ourproper-motion results do not confirm the arguments put forward by Noyola,Gebhardt & Bergmann to suspect an intermediate-mass black hole (IMBH) in OmegaCen. In Paper II we present new dynamical models for the high-quality datapresented here, with the aim of putting quantitative contraints on the mass ofany possible IMBH.

New Limits on an Intermediate Mass Black Hole in Omega Centauri: I. Hubble Space Telescope Photometry and Proper Motions