We describe a simple method for separating carbon nanotubes on the basis of their mesogenicity by fractionating biphasic aqueous suspensions within the Flory chimney of the lyotropic phase diagram. Macroscopic phase separation occurs on centrifuging the biphasic nanotube suspension or allowing it to stand. Long, straight nanotubes with higher mesogenicity (liquid crystalline forming ability) segregate preferentially to the liquid crystalline phase, whereas shorter nanotubes and impurities with lower mesogenicity segregate preferentially to the isotropic phase.