  We present the first detailed study of the RR Lyrae variable population in
the Local Group dSph/dIrr transition galaxy, Phoenix, using previously obtained
HST/WFPC2 observations of the galaxy. We utilize template light curve fitting
routines to obtain best fit light curves for RR Lyrae variables in Phoenix. Our
technique has identified 78 highly probable RR Lyrae stars (54 ab-type; 24
c-type) with about 40 additional candidates. We find mean periods for the two
populations of $\langle P_{ab}\rangle = 0.60 \pm 0.03$ days and $\langle
P_{c}\rangle = 0.353 \pm 0.002$ days. We use the properties of these light
curves to extract, among other things, a metallicity distribution function for
ab-type RR Lyrae. Our analysis yields a mean metallicity of $\langle
[Fe/H]\rangle = -1.68 \pm 0.06$ dex for the RRab stars. From the mean period
and metallicity calculated from the ab-type RR Lyrae, we conclude that Phoenix
is more likely of intermediate Oosterhoff type; however the morphology of the
Bailey diagram for Phoenix RR Lyraes appears similar to that of an Oosterhoff
type I system. Using the RRab stars, we also study the chemical enrichment law
for Phoenix. We find that our metallicity distribution is reasonably well
fitted by a closed-box model. The parameters of this model are compatible with
the findings of Hidalgo et al. (2009) further supporting the idea that Phoenix
appears to have been chemically enriched as a closed-box-like system during the
early stage of its formation and evolution.
