Comprehensive rotation-vibration line lists are presented for the two main isotopologues of methyl chloride, $^{12}$CH$_3{}^{35}$Cl and $^{12}$CH$_3{}^{37}$Cl. The line lists, OYT-35 and OYT-37, are suitable for temperatures up to $T=1200\,$K and consider transitions with rotational excitation up to $J=85$ in the wavenumber range $0$--$6400\,$cm$^{-1}$ (wavelengths $\lambda> 1.56\,\mu$m). Over 166 billion transitions between 10.2 million energy levels have been calculated variationally for each line list using a new empirically refined potential energy surface, determined by refining to 739 experimentally derived energy levels up to $J=5$, and an established {\it ab initio} dipole moment surface. The OYT line lists show excellent agreement with newly measured high-temperature infrared absorption cross-sections, reproducing both strong and weak intensity features across the spectrum. The line lists are available from the ExoMol database and the CDS database.
