We present a B, V color-magnitude diagram (CMD) of the Milky Way dwarf satellite Ursa Major II (UMa II), spanning the magnitude range from V ~ 15 to V ~ 23.5 mag and extending over a 18 {\times} 18 arcmin2 area centered on the galaxy. Our photometry goes down to about 2 magnitudes below the galaxy's main sequence turn-off, that we detected at V ~ 21.5 mag. We have discovered a bona-fide RR Lyrae variable star in UMa II, which we use to estimate a conservative dereddened distance modulus for the galaxy of (m-M)0 = 17.70{±}0.04{±}0.12 mag, where the first error accounts for the uncertainties of the calibrated photometry, and the second reflects our lack of information on the metallicity of the star. The corresponding distance to UMa II is 34.7 {±} 0.6 ({±} 2.0) kpc. Our photometry shows evidence of a spread in the galaxy subgiant branch, compatible with a spread in metal abundance in the range between Z=0.0001 and Z=0.001. Based on our estimate of the distance, a comparison of the fiducial lines of the Galactic globular clusters (GCs) M68 and M5 ([Fe/H]=-2.27 {±} 0.04 dex and -1.33 {±} 0.02 dex, respectively), with the position on the CMD of spectroscopically confirmed galaxy members, may suggest the existence of stellar populations of different metal abundance/age in the central region of UMa II. ; Comment: To appear in ApJ