Use of a single template-grown carbon nanotube as a separation column to separate attoliter volumes of binary mixtures of fluorescent dyes has been demonstrated. The cylindrical nanotube walls are used as stationary phase and the surface area is increased by growing smaller multi-walled carbon nanotubes within the larger nanotube column. Liquid-liquid extraction is performed to separate selectively soluble solutes in a solvent, and chromatographic separation is demonstrated using thin, long nanotubes coated inside with iron oxide nanoparticles. The setup is also used to determine the diffusion coefficient of a solute at the sub-micrometer scale. This study opens avenues for analytical chemistry in attoliter volumes of fluids for various applications and cellular analysis at the single cell level.