Phosphine-catalyzed highly enantioselective γ-additions of 5H-thiazol-4-ones and 5H-oxazol-4-ones to allenoates have been developed for the first time. With the employment of amino-acid derived bifunctional phosphines, a wide range of substituted 5H-thiazol-4-one and 5H-oxazol-4-one derivatives bearing heteroarom (S or O)-containing tertiary chiral centers were constructed in high yields and excellent enantioselectivities. The reported method provides a facile access to enantioenriched tertiary thioether/alcohols. The mechanism of γ-addition reaction was investigated by performing DFT calculations, and the hydrogen bonding interactions between the Brønsted acid moiety of the phosphine catalysts and the “C=O” unit of donor molecules were shown to be crucial in asymmetric induction.