We propose the concept of a "Galactic Habitable Zone" (GHZ). Analogous to the Circumstellar Habitable Zone (CHZ), the GHZ is that region in the Milky Way where an Earth-like planet can retain liquid water on its surface and provide a long-term habitat for animal-like aerobic life. In this paper we examine the dependence of the GHZ on Galactic chemical evolution. The single most important factor is likely the dependence of terrestrial planet mass on the metallicity of its birth cloud. We estimate, very approximately, that a metallicity at least half that of the Sun is required to build a habitable terrestrial planet. The mass of a terrestrial planet has important consequences for interior heat loss, volatile inventory, and loss of atmosphere. A key issue is the production of planets that sustain plate tectonics, a critical recycling process that provides feedback to stabilize atmospheric temperatures on planets with oceans and atmospheres. Due to the more recent decline from the early intense star formation activity in the Milky Way, the concentration in the interstellar medium of the geophysically important radioisotopes 40K, 235,238U, and 232Th has been declining relative to Fe, an abundant element in the Earth. Also likely important are the relative abundances of Si and Mg to Fe, which affects the mass of the core relative to the mantle in a terrestrial planet. All these elements and isotopes vary with time and location in the Milky Way; thus, planetary systems forming in other locations and times in the Milky Way with the same metallicity as the Sun will not necessarily form habitable Earth-like planets. As a result of the radial Galactic metallicity gradient, the outer limit of the GHZ is set primarily by the minimum required metallicity to build large terrestrial planets. Regions of the Milky Way least likely to contain Earth-mass planets are the halo (including globular clusters), the thick disk, and the outer thin disk. The bulge should contain Earth-mass planets, but stars in it have a mix of elements different from the Sun's. The existence of a luminosity-metallicity correlation among galaxies of all types means that many galaxies are too metal-poor to contain Earth-mass planets. Based on the observed luminosity function of nearby galaxies in the visual passband, we estimate that (1) the Milky Way is among the 1.3% most luminous (and hence most metal-rich) galaxies and (2) about 23% of stars in a typical ensemble of galaxies are more metal-rich than the average star in the Milky Way. The GHZ zone concept can be easily extrapolated to the universe as a whole, especially with regard to the changing star formation rate and its effect on metallicity and abundances of the long-lived radioisotopes.