  We introduce a hybrid approach to applying the density matrix renormalization
group (DMRG) to continuous systems, combining a grid approximation along one
direction with a finite Gaussian basis set along the remaining two directions.
This approach is especially useful for chain-like molecules, where the grid is
used in the long direction, and we demonstrate the approach with results for
hydrogen chains. The computational time for this system scales approximately
linearly with the length of the chain, as we demonstrate with minimal basis set
calculations with up to 1000 atoms, which are near-exact within the basis. The
linear scaling comes from the combination of localization of the basis and a
compression method with controlled accuracy for the long-ranged Coulomb terms
in the Hamiltonian.
