Optical nanostructures have enabled the creation of subdiffraction detection volumes for single-molecule fluorescence microscopy. Their applicability is extended by the ability to place molecules in the confined observation volume without interfering with their biological function. Here, we demonstrate that processive DNA synthesis thousands of bases in length was carried out by individual DNA polymerase molecules immobilized in the observation volumes of zero-mode waveguides (ZMWs) in high-density arrays. Selective immobilization of polymerase to the fused silica floor of the ZMW was achieved by passivation of the metal cladding surface using polyphosphonate chemistry, producing enzyme density contrasts of glass over aluminum in excess of 400:1. Yields of single-molecule occupancies of approximately 30% were obtained for a range of ZMW diameters (70-100 nm). Results presented here support the application of immobilized single DNA polymerases in ZMW arrays for long-read-length DNA sequencing.