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The prime focus CCD camera of the KPNO 4-m telescope has been used to image Andromeda III, a dwarf spheroidal galaxy companion to M31, in the $V$ and $I$ bands. The resulting color--magnitude diagram shows a well defined giant branch whose tip luminosity corresponds to that expected for an old metal-poor population at the distance of M31. By comparing these data with the giant branches of Galactic globular clusters, we determine that the abundance of And III is [Fe/H] = --2.0 $\pm$ 0.15; with this abundance And III lies on the luminosity--abundance relation defined by the Galactic dwarf spheroidal galaxies. There is some evidence for a small (0.16 $<$ $\sigma$([Fe/H]) $<$ 0.24) intrinsic abundance dispersion within And III, but we are unable to unambiguously establish its presence. A study of the And III $I$-band luminosity function yields a distance modulus ($m$--$M$)$_0$ of 24.4 $\pm$ 0.2 for this galaxy, and indicates that the fraction of intermediate-age (3 to 10 Gyr) population in And III is approximately 10 $\pm$ 10 percent. In all these aspects And III, like And I, is similar to the Galactic dwarf spheroidal systems, indicating that M31 and the Galaxy provided similar conditions for the evolution of such galaxies.
