Block copolymer Structures have been directed to assemble oil chemically patterned surfaces with the domain interfaces oriented perpendicular to the substrate. Such methods have been pursued for lithographic applications to achieve long-range order in the assembled structures and, potentially more important, provide nanometer-level control over the interfaces between Structures. The chemically striped surfaces used for the directed assembly of lamellae are patterned by top-down lithographic techniques and thus often have rough edges between the regions of different chemistry. Here we quantitatively characterize, using experiments and molecular-level simulations, the propagation of line edge roughness from the chemically patterned surfaces into the interfaces between domains of block copolymer lamellae as a function of the wavelength, amplitude, and geometry of the roughness. Two geometries of surface pattern roughness are considered with oscillatory neighboring interfaces that are either in-phase or out-of-phase. Block copolymer lamellae of poly(styrene-b/ock-methyl methacrylate) effectively self-corrected surface patterns with small wavelength in-phase and out-of-phase roughness such that little or no memory of the Substrate pattern roughness could be observed at the top surface of a 40 nm thin film. Larger wavelength in-phase roughness, and to a lesser extent larger wavelength out-of-phase roughness, propagated farther from the surface pattern such that the domain interfaces between block copolymer lamellae maintained the roughness throughout the film. These self-healing capabilities of block copolymers will be essential for lithographic applications with tight tolerances on line edge roughness and line width control, e.g., in patterning transistor gates.