Although the alkylation of an amine by an alkyl halide serves as a "textbook example" of a nucleophilic substitution reaction, the selective mono-alkylation of aliphatic amines by unactivated, hindered halides persists as a largely unsolved challenge in organic synthesis. We report herein that primary aliphatic amines can be cleanly mono-alkylated by unactivated secondary alkyl iodides in the presence of visible light and a copper catalyst. The method operates under mild conditions (-10 degrees C), displays good functional-group compatibility, and employs commercially available catalyst components. A trapping experiment with TEMPO is consistent with C-N bond formation via an alkyl radical in an out-of-cage process.