We present a linear-response theory for the thermopower of a single-electron transistor consisting of a superconducting island weakly coupled to two normal-conducting leads. The thermopower shows oscillations with the same periodicity as the conductance and is rather sensitive to the size of the superconducting gap Delta. In particular, the previously studied sawtooth-like shape of the thermopower for a normal-conducting single-electron device is qualitatively changed even for small gap energies.