  A new hot line list is calculated for $^{12}$CH$_4$ in its ground electronic
state. This line list, called 10to10, contains 9.8 billion transitions and
should be complete for temperatures up to 1500 K. It covers the wavelengths
longer than 1 $\mu$m and includes all transitions to upper states with energies
below $hc \cdot 18\,000$ cm$^{-1}$ and rotational excitation up to $J=39$. The
line list is computed using the eigenvalues and eigenfunctions of CH$_4$
obtained by variational solution of the Schr\"{o}dinger equation for the
rotation-vibration motion of nuclei employing program TROVE. An ab initio
dipole moment surface and a new 'spectroscopic' potential energy surface are
used. Detailed comparisons with other available sources of methane transitions
including HITRAN, experimental compilations and other theoretical line lists
show that these sources lack transitions both higher temperatures and near
infrared wavelengths. This line list is suitable for modelling atmospheres of
cool stars and exoplanets. It is available from the CDS database as well as at
www.exomol.com.
