  The host galaxies of the five local, z<0.25, long-duration gamma-ray bursts,
each of which had a well-documented associated supernova, are all faint and
metal-poor compared to the population of local star-forming galaxies. We
quantify this statement by using a previous analysis of star-forming galaxies
(z<0.2) from the Sloan Digital Sky Survey to estimate the fraction of local
star formation as a function of host galaxy oxygen abundance. We find that only
a small fraction (<25%) of current star formation occurs in galaxies with
oxygen abundance 12+log(O/H)<8.6, i.e., about half that of the Milky Way.
However, all five low-z GRB hosts have oxygen abundance below this limit, in
three cases very significantly so. If GRBs traced local star formation
independent of metallicity, the probability of obtaining such low abundances
for all five hosts would be P~0.1%. We conclude that GRBs trace only
low-metallicity star formation, and that the Milky Way has been too metal rich
to host long GRBs for at least the last several billion years. This result has
implications for the potential role of GRBs in mass extinctions, for searches
for recent burst remnants in the Milky Way and other large galaxies, for
non-detections of late radio emission from local core-collapse supernovae, and
for the production of cosmic rays in the local Universe. We also find that the
isotropic energy release of these five GRBs, E_iso, steeply decreases with
increasing host oxygen abundance, suggesting an upper metallicity limit for
``cosmological'' GRBs at ~0.15 Z_solar. (Abridged)
