There is significant interest in combining carbon nanotubes with semiconducting polymers for photovoltaic applications because of potential advantages from smaller exciton transport lengths and enhanced charge separation. However, to date, bulk heterojunction (BHJ) devices have demonstrated relatively poor efficiencies, and little is understood about the polymer/nanotube junction. To investigate this interface, we fabricate a planar nano-heterojunction comprising well-isolated millimeter-long single-walled carbon nanotubes underneath a poly(3-hexylthiophene) (P3HT) layer. The resulting junctions display photovoltaic efficiencies per nanotube ranging from 3% to 3.82%, which exceed those of polymer/nanotube BHJs by a factor of 50-100. The increase is attributed to the absence of aggregate formation in this planar device geometry. It is shown that the polymer/nanotube interface itself is responsible for exciton dissociation. Typical open-circuit voltages are near 0.5 V with fill factors of 0.25-0.3, which are largely invariant with the number of nanotubes per device and P3HT thickness. A maximum efficiency is obtained for a 60 nm-thick P3HT layer, which is predicted by a Monte Carlo simulation that takes into account exciton generation, transport, recombination, and dissociation. This platform is promising for further understanding the potential role of polymer/nanotube interfaces for photovoltaic applications.