The algorithm of two coupled SU(2) cosets is applied to the two coupled stretching modes of DCN. This is a simplest prototype with broken SU(2) symmetry for the study of chaotic molecular vibrations. The analysis shows that as the system energy increases, the vibrational motion changes from regularity to chaos. Notably, trajectories of period-3 on the Poincare surfaces of section are observed. This implies chaos according to Sarkovskii's theorem. It is also demonstrated that the excitation of D-C and not C-N is crucial for the occurrence of chaos.