We report the observation of an order of magnitude enhancement of the thermoelectric figure of merit (ZT = 0.36) in topological insulator Bi1.5Sb0.5Te1.7Se1.3 nanowires at 300 K as compared with the bulk specimen (ZT = 0.028). The enhancement was primarily due to an order of magnitude increase in the electrical conductivity of the surface-dominated transport and thermally activated charge carriers in the nanowires. Magnetoresistance analysis revealed the presence of Dirac electrons and determined that the Fermi level was near the conduction band edge. This may be the first thermoelectric measurement of samples with a chemical potential in the gap of a topological insulator without gate tuning, and provides an opportunity to study the contribution of surface states to the Seebeck coefficient and resistivity without concern for the complex effect of band bending.