We report solid-phase epitaxy of amorphous Si (a-Si) shells using crystalline Si (c-Si) nanowire cores as seed templates. The c-Si core/a-Si shell nanowire heterostructures were in situ synthesized via a two-step chemical vapor deposition: the Au-catalytic decomposition of SiH(4) for the core c-Si nanowires and the subsequent homogeneous decomposition of SiH(4) at higher temperatures for the a-Si shells. Upon thermal annealing above 600 degrees C, the a-Si shells crystallize into c-Si shells from c-Si core nanowires in an epitaxial fashion. We discuss the crystallization kinetics of a-Si shells within the frame of Gibbs-Thomson effects arising from the finite size of nanowire seeds.