Intense well-polarized second harmonic light was generated by para-Nitroaniline self-assembled thin films in different polymeric host matrices. The large area films of the organic chromophore with micron thickness were produced using a modified version of capillary growth. Analysis of the generated second harmonic light indicates that the para-Nitroaniline molecules, which nominally crystalize in a centrosymmetric space group, were organized into structures with an appreciable second order susceptibility dominated by a single tensor element. Under the best conditions, the film's effective second order optical susceptibility is slightly greater than that of beta barium borate for incident light at 800 nm. Generalizing this approach to a broad range of organic molecules with strong individual molecular second order nonlinear responses, but which ordinarily form centrosymmetric organic crystals, could open a new pathway for the fabrication of efficient thin film second harmonic light generators.