The coexistence in Te-rich CdTe of substitutional Cl-dopants, ClTe, which act as donors, and Cd vacancies, VCd−1, which act as electron traps, was studied from first principles utilising the HSE06 hybrid functional. We find ClTe to preferably bind to VCd−1 and to form an acceptor complex, (ClTe–VCd)−1. The complex has a (0,-1) charge transfer level close to the valence band and shows no trap state (deep level) in the band gap. During the complex formation, the defect state of VCd−1 is annihilated and leaves the Cl-doped CdTe bandgap without any trap states (self-purification). We calculate Cl-doped CdTe to be semi-insulating with a Fermi energy close to midgap. We calculate the formation energy of the complex to be sufficiently low to allow for spontanous defect formation upon Cl-doping (self-compensation). In addition, we quantitatively analyse the geometries, DOS, binding energies and formation energies of the (ClTe–VCd) complexes.