We have computed cross sections for charge transfer between C³⁺(1s²2s ²S) and H(1s ²S) for relative collision energies in the range 0.004<or=E<or=90 eV amu^-1. The molecular orbital data were taken from Errea et al. (1991a); both triplet and singlet spin symmetries were considered. In order to extend the calculations to low energies, where the rate coefficient is required for astrophysical applications, a quantal treatment of the molecular dynamics was adopted. Comparison is made with previous calculations and with experiment, including the recent measurements of Havener et al. (1995). At low energies, cross sections for electron capture from deuterium are found to be significantly smaller than the corresponding ones for hydrogen owing to the dynamical effect of the greater reduced mass.