Primal discontinuous Galerkin (DG) methods, including the Oden-Babuška-Baumann version of DG, are formulated for solving multicomponent reactive transport problems in porous media. Using the information of chemical stoichiometry, an efficient approach is proposed for a special case of multicomponent reactive transport without immobile species. A priori error analysis is conducted to establish the convergence of DG methods for multicomponent reactive transport systems, which is optimal in h and nearly optimal in p.