We investigate the atomic geometry and energetics of Cl-related defects in ZnTe through first-principles pseudopotential calculations. We find a type of defect that results from large lattice relaxations, with C-3 nu symmetry and triple broken bonds around the Cl impurity at a Zn sublattice site. The triple-broken-bond structure of Cl-Zn behaves as an acceptor and this defect is more stable than the DX-like broken-bond state of Cl-Te. Thus, we suggest that the triple-broken-bond centers are very effective in donor compensation, particularly in heavily Cl-doped ZnTe as well as in samples grown under Te-rich conditions.