  Measurements of [C/Fe], [Ca/H], and [Fe/H] have been derived from Keck I
LRISb spectra of 35 giants in the Draco dwarf spheroidal galaxy. The iron
abundances are derived by a spectrum synthesis modeling of the wavelength
region from 4850 to 5375 A, while calcium and carbon abundances are obtained by
fitting the Ca II H and K lines and the CH G band respectively. A range in
metallicity of -2.9 <= [Fe/H]} <= -1.6 is found within the giants sampled, with
a good correlation between [Fe/H] and [Ca/H]. The great majority of stars in
the sample would be classified as having weak absorption in the lambda 3883 CN
band, with only a small scatter in band strengths at a given luminosity on the
red giant branch. In this sense the behavior of CN among the Draco giants is
consistent with the predominantly weak CN bands found among red giants in
globular clusters of metallicity [Fe/H] < -1.8. Over half of the giants in the
Draco sample have [Fe/H] > -2.25, and among these there is a trend for the
[C/Fe] abundance to decrease with increasing luminosity on the red giant
branch. This is a phenomenon that is also seen among both field and globular
cluster giants of the Galactic halo, where it has been interpreted as a
consequence of deep mixing of material between the base of the convective
envelope and the outer limits of the hydrogen-burning shell. However, among the
six Draco giants observed that turn out to have metallicities -2.65 < [Fe/H] <
-2.25 there is no such trend seen in the carbon abundance. This may be due to
small sample statistics or primordial inhomogeneities in carbon abundance among
the most metal-poor Draco stars. We identify a potential carbon-rich extremely
metal-poor star in our sample. This candidate will require follow up
observations for confirmation.
