A domain decomposition method for the Poisson-Boltzmann solvation model that is widely used in computational chemistry is proposed. This method, called ddLPB for short, solves the linear Poisson-Boltzmann equation defined in 3D Euclidean space using the van der Waals cavity as the solute cavity. The Schwarz domain decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled subequations in balls. A series of numerical experiments is presented to test the robustness and the efficiency of this method including comparisons with some existing methods. We observe exponential convergence of the solvation energy with respect to the number of degrees of freedom which allows this method to reach the required level of accuracy when coupling with quantum mechanical descriptions of the solute.