The development of catalytic and enantioselective transformations for the synthesis of all-carbon quaternary stereocenters has long been recognized as a significant challenge in organic synthesis. While considerable progress has been made in asymmetric allylations, their potential to functionalize the commonly used synthon, epoxide, remains largely underexplored. Here we demonstrate the first highly regio- and enantioselective allylation of epoxides that delivers a range of quaternary stereocenters in the face of potentially problematic elimination and protonation reactions. The reaction proceeds via a radical approach under mild conditions and benefits from the use of earth-abundant titanium with a highly sophisticated salen ligand, which facilitates remarkable enantiocontrol and suppresses undesired side reactions. The resulting allylation products are multifunctional building blocks that can be elaborated chemo- and stereoselectively to a broad array of stereodefined structural motifs.