We show how state-dependent optical potentials can be used to trap a pair of molecules in different internal states at a separation much smaller than the wavelength of the trapping light. This close spacing greatly enhances the
dipole-dipole interaction and we show how it can be used to implement two-qubit gates between molecules that are 100 times faster than existing protocols and than rotational coherence times already demonstrated. We analyze complications due to hyperfine structure, tensor light shifts, photon scattering and collisional loss, and conclude that none is a barrier to implementing the scheme.