We synthesized wurtzite CuInS2 nanorods (NRs) by colloidal solution-phase growth. We discovered that the growth process starts with nucleation of Cu2S nanodisks, followed by epitaxial overgrowth of CuInS2 NRs onto only one face of Cu2S nanodisks, resulting in biphasic Cu2S-ClSu heterostructured NRs. The phase transformation of biphasic Cu2S-CuInS2 into monophasic CuInS2 NRs occurred with growth progression. The observed epitaxial overgrowth and phase transformation is facile for three reasons. First, the sharing of the sulfur sublattice by the hexagonal chalcocite Cu2S and wurtzite CuInS2 minimizes the lattice distortion. Second, Cu2S is in a superionic conducting state at the growth temperature of 250 degrees C wherein the copper ions move fluidly. Third, the size of the Cu2S nanodisks is small, resulting in fast phase transformation. Our results provide valuable insight into the controlled solution growth of ternary chalcogenide nanoparticles and will aid in the development of solar cells using ternary I-III-VI2 semiconductors.