The ion-molecule reaction C + H3+ --> CH(+) + H2 has not been studied in the laboratory but is thought to be important in the gas phase synthesis of organic molecules in dense interstellar clouds. We have studied this reaction theoretically by performing quantum chemical ab initio calculations on the potential surface. We find that there is no activation barrier to the reaction and that it proceeds smoothly to the first excited electronic state of CH+. The rate coefficient as a function of temperature can then be estimated using the proper long-range potentials. The rate coefficient at 10 K is calculated to be 2.9 x 10(-9) cm3 s-1.