In III-V and II-VI semiconductors, certain nominally electron-donating impurities do not release electrons but instead form deep electron-traps known as "DX centers." While in these compounds, such traps occur only after the introduction of foreign impurity atoms, we find from first-principles calculations that in ternary I-III-VI2 chalcopyrites like CuInSe2 and CuGaSe2, DX-like centers can develop without the presence of any extrinsic impurities. These intrinsic DX centers are suggested as a cause of the difficulties to maintain high efficiencies in CuInSe2-based thin-film solar-cells when the band gap is increased by addition of Ga.