We present a numerical implementation of the quantum chemistry density matrix renormalization group (DMRG) using the hybrid discrete variable representation (DVR)/Gaussian basis set. The z-axis of real space is discretized by a DVR basis set and each transversal plane is described by the eigenstates of the transversal core Hamiltonian, represented in a set of primitive Gaussian basis functions. Such a hybrid basis can reduce the computation of two-electron repulsion integrals. One main advantage of using the local DVR basis sets over finite-difference methods for real space discretization is that the kinetic energy operator matrix elements can be computed exactly. This method is first applied to a one-dimensional pseudo-hydrogen chain under screened Coulomb potential and then to a realistic hydrogen chain, whereby the DMRG/DVR results are comparable in accuracy to the full configuration interaction results.