The host galaxies of the five local, z leq 0.25, long-duration gamma-ray bursts (GRBs 980425, 020903, 030329, 031203 and 060218), 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 (0.005<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. Our results agree with theoretical models that tie GRBs to rapidly spinning progenitors, which require minimal angular momentum loss in stellar winds. We also find that the isotropic energy release of these five GRBs, Eiso, steeply decreases with increasing host oxygen abundance. This might further indicate that (low) metallicity plays a fundamental physical role in the GRB phenomenon, and suggesting an upper metallicity limit for ``cosmological'' GRBs at appro 0.15 Zodot.