We report empirical observations of magnetic island heteroclinic bifurcation for the first time. This behavior is observed in interacting coupled 2/1 tearing modes in the core of a DIII-D tokamak plasma. Poincaré maps constrained by measured magnetic amplitudes and phasing show bifurcation from heteroclinic to homoclinic topology in the 2/1 island as the 4/2 relative amplitude (R_{4/2}) decreases. Initially, the local electron temperature peak in the 2/1 island splits, consistent with two O points. As R_{4/2} decreases a single peak forms, consistent with one O point. These call for developing tearing stability theory and control solutions for heteroclinic islands in tokamaks.