We present a theory of the phonon-drag Seebeck coefficient in nondegenerate semiconductors, and apply it to silicon for temperatures 30 < T < 300 K. Our calculation uses only parameters from the literature, and previous calculations of the phonon lifetime. We find excellent agreement with the measurements of Geballe and Hull [Phys. Rev. 98, 940 (1955)]. The phonon-drag term dominates at low temperature, and shows an important dependence on the dimensions of the experimental sample.