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We present new near-infrared ($JHK_s$) time-series observations of RR Lyraevariables in the Messier 3 (NGC 5272) globular cluster using the WIRCaminstrument at the 3.6-m Canada France Hawaii Telescope. Our observations covera sky area of $\sim 21'\times 21'$ around the cluster center and provide anaverage of twenty epochs of homogeneous $JHK_s$-band photometry. Newhomogeneous photometry is used to estimate robust mean magnitudes for 175fundamental-mode (RRab), 47 overtone-mode (RRc), and 11 mixed-mode (RRd)variables. Our sample of 233 RR Lyrae variables is the largest thus farobtained in a single cluster with time-resolved, multi-band near-infraredphotometry. Near-infrared to optical amplitude ratios for RR Lyrae in Messier 3exhibit a systematic increase moving from RRc to short-period ($P < 0.6$~days)and long-period ($P \gtrsim 0.6$~days) RRab variables. We derive $JHK_s$-bandPeriod--Luminosity relations for RRab, RRc, and the combined sample ofvariables. Absolute calibrations based on the theoretically predictedPeriod--Luminosity--Metallicity relations for RR Lyrae stars yield a distancemodulus, $\mu = 15.041 \pm 0.017~(\textrm{statistical}) \pm0.036~(\textrm{systematic})$~mag, to Messier 3. When anchored to trigonometricparallaxes for nearby RR Lyrae stars from the {\it Hubble Space Telescope} andthe {\it Gaia} mission, our distance estimates are consistent with thoseresulting from the theoretical calibrations, albeit with relatively largersystematic uncertainties.

Near-infrared Census of RR Lyrae variables in the Messier 3 globular cluster and the Period--Luminosity Relations