A new protocol for amide-directed Cu-catalyzed aminoalkylation of unactivated alkenes using cyclobutanone oxime esters as alkyl radical donors is developed. Both primary and secondary alkyl groups can be selectively installed at the C4 position of terminal or cis-internal 3-alkenamides in moderate to good yield. This reaction offers a useful method for the diastereoselective synthesis of β-lactams bearing 4-cyanoalkyl β-substituents. The use of a weakly coordinating counteranion as the Cu catalyst is critical for the formation of β-lactam products.