Extrusion, electrospinning, and microdrawing are widely used to create fibrous polymer mats, but these approaches offer limited access to oriented arrays of nanometer-scale fibers with controlled size, shape, and lateral organization. We show that chemical vapor polymerization can be performed on surfaces coated with thin films of liquid crystals to synthesize organized assemblies of end-attached polymer nanofibers. The process uses low concentrations of radical monomers formed initially in the vapor phase and then diffused into the liquid-crystal template. This minimizes monomer-induced changes to the liquid-crystal phase and enables access to nanofiber arrays with complex yet precisely defined structures and compositions. The nanofiber arrays permit tailoring of a wide range of functional properties, including adhesion that depends on nanofiber chirality.