We have discovered 20 dwarf Cepheids (DCs) in the Carina dwarf spheroi
dal galaxy from an analysis of individual CCD images obtained for a de
ep photometric study of the system. These short-period pulsating varia
ble stars are by far the most distant (similar to 100 kpc) and faintes
t (V similar to 23.0) DCs known. The Carina DCs obey a well-defined pe
riod-luminosity relation, allowing us to readily distinguish between o
vertone and fundamental pulsators in nearly every case. Unlike RR Lyra
e stars, the pulsation mode turns out to be uncorrelated with light-cu
rve shape, and the overtone pulsators do not tend toward shorter perio
ds compared with the fundamental pulsators. Using the period-luminosit
y relations from Nemec, Nemec, & Lutz and McNamara, we derive (m - M)(
0) = 20.06 +/- 0.12, for E(B - V) = 0.025 and [Fe/H] = -2.0, in good a
greement with recent, independent estimates of the distance/reddening
of Carina. The error reflects the uncertainties in the DC distance sca
le, and in the metallicity and reddening of Carina. The frequency of D
Cs among upper-main-sequence stars in Carina is approximately 3%. The
ratio of dwarf Cepheids to RR Lyrae stars in Carina is 0.13 +/- 0.10,
though this result is highly sensitive to the star formation history o
f Carina and the evolution of the horizontal branch. We discuss how DC
s may be useful to search effectively for substructure in the Galactic
halo out to Galactocentric distances of less than or similar to 100 k
pc.