We present new Near-Infrared (J,K) magnitudes for 114 RR Lyrae stars in the globular cluster Omega Cen (NGC 5139) which we combine with data from the literature to construct a sample of 180 RR Lyrae stars with J and K mean magnitudes on a common photometric system. This is presently the largest such sample in any stellar system. We also present updated predictions for J,K-band Period-Luminosity relations for both fundamental and first-overtone RR Lyrae stars, based on synthetic horizontal branch models with metal abundance ranging from Z=0.0001 to Z=0.004. By adopting for the Omega Cen variables with measured metal abundances an alpha-element enhancement of a factor of 3 (about 0.5 dex) with respect to iron we find a true distance modulus of 13.70 (with a random error of 0.06 and a systematic error of 0.06), corresponding to a distance d=5.5 Kpc (with both random and systematic errors equal to 0.03 Kpc). Our estimate is in excellent agreement with the distance inferred for the eclipsing binary OGLEGC-17, but differ significantly from the recent distance estimates based on cluster dynamics and on high amplitude Delta Scuti stars.
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