We study the thermopower of a quantum dot weakly coupled to two reservoirs by tunnel junctions. At low temperatures the transport through the dot is suppressed by charging effects (Coulomb blockade). As a result the thermopower shows an oscillatory dependence on the gate voltage. We study this dependence in the limit of low temperatures where transport through the dot is dominated by the processes of inelastic cotunneling. We also obtain a crossover formula for intermediate temperatures which connects our cotunneling results to the known sawtooth behavior in the sequential tunneling regime. As the temperature is lowered, the amplitude of thermopower oscillations increases, and their shape changes qualitatively.