  We have performed the first study of the variable star population of Ursa
Major I (UMa I), an ultra-faint dwarf satellite recently discovered around the
Milky Way by the Sloan Digital Sky Survey. Combining time series observations
in the B and V bands from four different telescopes, we have identified seven
RR Lyrae stars in UMa I, of which five are fundamental-mode (RRab) and two are
first-overtone pulsators (RRc). Our V, B-V color-magnitude diagram of UMa I
reaches V~23 mag (at a signal-to-noise ratio of ~ 6) and shows features typical
of a single old stellar population. The mean pulsation period of the RRab stars
<Pab> = 0.628, {\sigma} = 0.071 days (or <Pab> = 0.599, {\sigma} = 0.032 days,
if V4, the longest period and brightest variable, is discarded) and the
position on the period-amplitude diagram suggest an Oosterhoff-intermediate
classification for the galaxy. The RR Lyrae stars trace the galaxy horizontal
branch at an average apparent magnitude of <V(RR)> = 20.43 +/- 0.02 mag
(average on 6 stars and discarding V4), giving in turn a distance modulus for
UMa I of (m-M)0 = 19.94 +/- 0.13 mag, distance d= 97.3 +6.0/-5.7 kpc, in the
scale where the distance modulus of the Large Magellanic Cloud is 18.5 +/- 0.1
mag. Isodensity contours of UMa I red giants and horizontal branch stars
(including the RR Lyrae stars identified in this study) show that the galaxy
has an S-shaped structure, which is likely caused by the tidal interaction with
the Milky Way. Photometric metallicities were derived for six of the UMa I RR
Lyrae stars from the parameters of the Fourier decomposition of the V-band
light curves, leading to an average metal abundance of [Fe/H] = -2.29 dex
({\sigma} = 0.06 dex, average on 6 stars) on the Carretta et al. metallicity
scale.
