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. Here 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 phosphine can accumulate to detectable concentrations on planets with surface production fluxes of 10 10 -10 14 cm -2 s -1 (corresponding to surface concentrations of 10s of ppb to 100s of ppm), depending on atmospheric composition, and UV irradiation. While high, the surface flux values are comparable to the global terrestrial production rate of methane, or CH4 (10 11 cm -2 s -1 ) and below the maximum local terrestrial PH3 production rate (10 14 cm -2 s -1 ). As with other gases, PH3 can more readily accumulate on low-UV planets, e.g. planets orbiting quiet M-dwarfs or with a photochemically generated UV shield.If detected, 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. PH3 also has three strong spectral features such that in any atmosphere scenario one of the three will be unique compared to other dominant spectroscopic molecules. PH3's weakness as a biosignature gas is its high reactivity, requiring high outgassing rates for detectability. We calculate that tens of hours of JWST 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.