The well defined shape and size of carbon nanotubes (CNTs) makes them attractive candidates for theoretical and experimental studies of various nanoscopic phenomena such as protection and confinement of molecular species as well as transport of molecules through their interior pores. Here we investigate solute partitioning and transport using molecular dynamics simulations of CNTs in mixtures of hydrophobic solutes and water. The hydrophobic pores of CNTs provide a favorable environment for partitioning of hydrophobic solutes. We find that the transfer of a methane molecule from aqueous solution into the CNT interior is favored by about 16 kJ/mol of free energy. In 50 molecular dynamics simulations, we observe that methane molecules replace water molecules initially inside the nanotubes, and completely fill their interior channels over a nanosecond time scale. Once filled with methane molecules, the nanotubes are able to transport methane from one end to the other through successive methane uptake and release events at the tube ends. We estimate a net rate of transport of about 11 methane molecules per nanotube and nanosecond for a 1 mol/L methane concentration gradient. This concentration-corrected rate of methane transport even exceeds that of water through nanotubes (similar to1 per nanosecond at a 1 mol/L osmotic gradient). These results have implications for the design of molecule-selective CNT devices that may act through mechanisms similar to those of biological transmembrane channels.