Nonradiative recombination in Cu(In,Ga)Se2 (CIGS) solar cells has long been attributed to the antisite defects MCu (M = In, Ga), but the underlying mechanism is still elusive. Using rigorous first-principles calculations, we demonstrate that the antisites themselves cannot capture holes and hence cannot lead to efficient carrier recombination. Instead, internal conversion in the neutral charge state to the distorted DX center configuration opens an efficient hole-capture pathway. After hole capture, the positive charge state returns to the normal antisite configuration without any barrier to complete the entire recombination cycle. Our results show that the DX center is thermally accessible in CuGaSe2, but not in CuInSe2, due to its rather low conduction-band minimum; thus, the recombination rate in CIGS is composition dependent. These insights clarify the nonradiative recombination mechanism in ternary chalcopyrites and provide a guideline for composition engineering to enable the optimal performance of CIGS solar cells.