We have prepared 5 nm diameter, micrometer long tetra(p-phenylenevinylene) (OPV)-based nanofibers on a graphite surface. The fluorescence emission of an individual fiber shows a profound polarization over its entire length that directly corresponds to its orientation on the substrate. Quantitative analysis of the fluorescence polarization, including the depolarizing effect of the underlying graphite, evidences the high degree of organization within chiral fibers with the OPV molecules perpendicular to the fiber axis. The control of the internal order within self-assembled fibers, and the ability to measure it, is a crucial step to obtain uniform organic fibers that can be applied in nanosized electronics at room temperature.