We present the first measurements of the temperature and oxygen-doping dependences of thermoelectric power in the ab plane of untwinned YBa2Cu3O7-delta (delta almost equal to 0.10) for T less than or equal to 330 K. Employing a two-band model and measured electrical resistivities, we derive the chain and plane components of the thermopower, S(ch) and S(pl). The behavior of S(ch) indicates that some of the chain conduction occurs via carriers in a narrow band. S(pl)(T) is similar to the in-plane thermopower of the other cuprates, suggesting a "universal" behavior for the CuO2 planes. The results are discussed with reference to the known Fermi surface.