Estimates of the rate constants for the radiative association of methylidene radicals (CH) with molecular hydrogen (H-2), CH + H-2 --> CH3 + hv, are reported for the temperature range (10-100 K) prevalent in dense interstellar clouds. These estimates are based on (1) new and extensive laboratory experiments on the collisional association of CH and H-2, CH + H-2(+M) --> CH3(+M), including measurements of rate constants down to temperatures as low as 53 K; and (2) calculations of the rate constants for both radiative and collisional association based on methods originally proposed by Troe, modified to include the effects of quantum mechanical tunneling as proposed by Smith. The results suggest that radiative association of CH with H-2 may be a significant reaction in interstellar clouds because of the high abundance of H-2. Although the association of CH with H-2 seems likely to be only a minor route for the removal of CH radicals, the reaction does provide a pathway to the formation of CH3, and subsequently simple hydrocarbons, which may be of comparable importance to other mechanisms based on ion-molecule chemistry. In addition, measured and estimated low temperature rate coefficients are reported for isotope exchange between CH, CD and H-2, HD, D-2 which may be relevant to isotopic fractionation in interstellar clouds.