We present detailed ultraviolet, optical and near-infrared light curves of the Type Ia supernova (SN) 2012fr, which exploded in the Fornax cluster member NGC 1365. These precise high-cadence light curves provide a dense coverage of the flux evolution from $-$12 to $+$140 days with respect to the epoch of $B$-band maximum (tmax). Supplementary imaging at the earliest epochs reveals an initial slow, nearly linear rise in luminosity with a duration of $sim$2.5 days, followed by a faster rising phase that is well reproduced by an explosion model with a moderate amount of $^{56}$Ni mixing in the ejecta. From an analysis of the light curves, we conclude: $(i)$ explosion occurred $< 22$ hours before the first detection of the supernova, $(ii)$ the rise time to peak bolometric ($lambda > 1800 $AA) luminosity was $16.5 pm 0.6$ days, $(iii)$ the supernova suffered little or no host-galaxy dust reddening, $(iv)$ the peak luminosity in both the optical and near-infrared was consistent with the bright end of normal Type Ia diversity, and $(v)$ $0.60 pm 0.15 M_{odot}$ of $^{56}$Ni was synthesized in the explosion. Despite its normal luminosity, SN 2012fr displayed unusually prevalent high-velocity ion{Ca}{2} and ion{Si}{2} absorption features, and a nearly constant photospheric velocity of the ion{Si}{2} $lambda$6355 line at $sim$12,000 kms beginning $sim$5 days before tmax. Other peculiarities in the early phase photometry and the spectral evolution are highlighted. SN 2012fr also adds to a growing number of Type Ia supernovae hosted by galaxies with direct Cepheid distance measurements.
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