Spontaneous exfoliation of single-walled carbon nanotubes on dilution of dispersions in a common solvent, N-methyl-pyrrolid one, is demonstrated. The free-energy of mixing is negative, confirming athermal solubility. Scanning tunneling microscopy measurements show physisorption of the solvent to the nanotube (see figure). Experiments, supported by a simple model, show that successful solvents for nanotubes are those with surface tensions close to that of graphite.