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A comprehensive hot line list is calculated for $^{31}$PH$_3$ in its groundelectronic state. This line list, called SAlTY, contains almost 16.8 billiontransitions between 7.5 million energy levels and it is suitable for simulatingspectra up to temperatures of 1500~K. It covers wavelengths longer than1~$\mu$m and includes all transitions to upper states with energies below $hc\cdot 18\,000$~cm$^{-1}$ and rotational excitation up to $J=46$. The line listis computed by variational solution of the Schr\"odinger equation for therotation-vibration motion employing the nuclear-motion program TROVE. Apreviously reported {\it ab initio} dipole moment surface is used as well as anupdated `spectroscopic' potential energy surface (PES), obtained by refining anexisting \textit{ab initio} surface through least-squares fitting to theexperimentally derived energies. Detailed comparisons with other availablesources of phosphine transitions confirms SAlTY's accuracy and illustrates theincompleteness of previous experimental and theoretical compilations fortemperatures above 300 K. Atmospheric models are expected to severelyunderestimate the abundance of phosphine in disequilibrium environments, and itis predicted that phosphine will be detectable in the upper troposphere of manysubstellar objects. This list is suitable for modelling atmospheres of manyastrophysical environments, namely carbon stars, Y dwarfs, T dwarfs, hotJupiters and solar system gas giant planets. It is available in full assupplementary data to the article and at \url{www.exomol.com}.

ExoMol line lists VII: The rotation-vibration spectrum of phosphine up to 1500 K