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 1500K. It covers the wavelengths longer than 1{mu}m and includes all transitions to upper states with energies below hc 18000cm^-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 equation for the rotation-vibration motion of nuclei employing program TROVE and a new 'spectroscopic' potential energy surface (PES) obtained by refining an ab initio PES (CCSD(T)-F12c/aug-cc-pVQZ) in a least-squares fitting to the experimentally derived energies with J=0, 1, 2, 3, 4 as extracted from the HITRAN database. The dipole transition probabilities are represented by the Einstein-A coefficients obtained using a previously reported ab initio dipole moment surface (CCSD(T)-F12c/aug-cc-pVTZ). 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. The 10to10 line list is suitable for modelling atmospheres of cool stars and exoplanets.