Nanocarbon-based photovoltaics offer a promising new architecture for the next generation of solar cells. We demonstrate that a key factor determining the efficiency of single-walled carbon nanotube (SWCNT)/fullerene devices is the chirality of the SWCNT. This is shown via current density vs voltage measurements of nanocarbon devices prepared with (9,7), (7,6) and (6,5) SWCNTs, as well as density-functional theory (DFT) density of states calculations of C60 adsorbed onto the corresponding SWCNTs. The trends in efficiency are rationalized in terms of the relative energies of the fullerene and SWCNT conduction band energy levels.