A long-term goal of exoplanet studies is the identification and detection of biosignature gases. Beyond the most discussed biosignature gas O2, only a handful of gases have been considered in detail. In this study, we evaluate phosphine (PH3). On Earth, PH3 is associated with anaerobic ecosystems, and as such, it is a potential biosignature gas in anoxic exoplanets. We simulate the atmospheres of habitable terrestrial planets with CO2- and H2-dominated atmospheres and find that PH3 can accumulate to detectable concentrations on planets with surface production fluxes of 1010 to 1014 cm-2 s-1 (corresponding to surface concentrations of 10s of ppb to 100s of ppm), depending on atmospheric composition and ultraviolet (UV) irradiation. While high, the surface flux values are comparable to the global terrestrial production rate of methane or CH4 (1011 cm-2 s-1) and below the maximum local terrestrial PH3 production rate (1014 cm-2 s-1). As with other gases, PH3 can more readily accumulate on low-UV planets, for example, planets orbiting quiet M dwarfs or with a photochemically generated UV shield. PH3 has three strong spectral features such that in any atmosphere scenario one of the three will be unique compared with other dominant spectroscopic molecules. Phosphine's weakness as a biosignature gas is its high reactivity, requiring high outgassing rates for detectability. We calculate that tens of hours of JWST (James Webb Space Telescope) time are required for a potential detection of PH3. Yet, because PH3 is spectrally active in the same wavelength regions as other atmospherically important molecules (such as H2O and CH4), searches for PH3 can be carried out at no additional observational cost to searches for other molecular species relevant to characterizing exoplanet habitability. Phosphine is a promising biosignature gas, as it has no known abiotic false positives on terrestrial planets from any source that could generate the high fluxes required for detection.