A long-term goal of exoplanet studies is the identification and detection of biosignature gases. Beyond the most discussed biosignature gas O$_2$, only a handful of gases have been considered in detail. Here we evaluate phosphine (PH$_3$). On Earth, PH$_3$ is associated with anaerobic ecosystems, and as such is a potential biosignature gas on anoxic exoplanets. We simulate CO$_2-$ and H$_2-$dominated habitable terrestrial planet atmospheres. We find that PH$_3$ 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 flux. While high, such surface fluxes are comparable to the global terrestrial production rate of CH$_4$ (10$^{11}$ cm$^{-2}$ s$^{-1}$) and below the maximum local terrestrial PH$_3$ production rate (10$^{14}$ cm$^{-2}$ s$^{-1}$). As with other gases, PH$_3$ can more readily accumulate on low-UV planets, e.g. planets orbiting quiet M-dwarfs or with a photochemical UV shield. If detected, PH$_3$ is a promising biosignature gas, as it has no known abiotic false positives on terrestrial planets that could generate the high fluxes required for detection. PH$_3$ also has 3 strong spectral features such that in any atmosphere scenario 1 of the 3 will be unique compared to other dominant spectroscopic molecules. PH$_3$s weakness as a biosignature gas is its high reactivity, requiring high outgassing for detectability. We calculate that 10s of hours of JWST time are required for a potential detection of PH$_3$. Yet because PH$_3$ is spectrally active in the same wavelength regions as other atmospherically important molecules (e.g., H$_2$O and CH$_4$), searches for PH$_3$ can be carried out at no additional observational cost to searches for other molecules relevant to exoplanet habitability.
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