We synthesized wurtzite CuInS(2) nanorods (NRs) by colloidal solution-phase growth. We discovered that the growth process starts with nucleation of Cu(2)S nanodisks, followed by epitaxial overgrowth of CuInS(2) NRs onto only one face of Cu(2)S nanodisks, resulting in biphasic Cu(2)S-CISu heterostructured NRs. The phase transformation of biphasic Cu(2)S-CuInS(2) into monophasic CuInS(2) 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 Cu(2)S and wurtzite CuInS(2) minimizes the lattice distortion. Second, Cu(2)S 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 Cu(2)S 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-VI(2) semiconductors.