The X-ray emission by hot gas at the centers of clusters of galaxies i
s commonly modeled assuming the existence of steady state, inhomogeneo
us cooling flows. We derive the metallicity profiles of the intraclust
er medium expected from such models. The inflowing gas is chemically e
nriched by Type Ia supernovas and stellar mass loss in the outer parts
of the central galaxy, which may give rise to a substantial metallici
ty gradient. The amplitude of the expected metallicity enhancement tow
ard a cluster's center is proportional to the ratio of the central gal
axy's luminosity to the mass-inflow rate. The metallicity of the hotte
r phases is expected to be higher than that of the colder, denser phas
es. The metallicity profile expected for the Centaurus Cluster is in g
ood agreement with the metallicity gradient recently inferred from ASC
A measurements. However, current data do not rule out alternative mode
ls in which cooling is balanced by some heat source. The metallicity g
radient does not need to be present in all clusters, depending on the
recent merger history of the gas around the central cluster galaxy and
on the ratio of the stellar mass in the central galaxy to the gas mas
s in the cooling flow.