We introduce a method, based on a novel thermodynamic integration scheme, to extract the Flory-Huggins χ parameter as small as 10^{-3}kT for polymer blends from molecular dynamics (MD) simulations. We obtain χ for the archetypical coarse-grained model of nonpolar polymer blends: flexible bead-spring chains with different Lennard-Jones interactions between A and B monomers. Using these χ values and a lattice version of self-consistent field theory (SCFT), we predict the shape of planar interfaces for phase-separated binary blends. Our SCFT results agree with MD simulations, validating both the predicted χ values and our thermodynamic integration method. Combined with atomistic simulations, our method can be applied to predict χ for new polymers from their chemical structures.