Radical‐involved arylative cross‐coupling reactions have recently emerged as an attractive strategy to access valuable aryl‐substituted motifs. However, there still exist several challenges such as limited scope of radical precursors/acceptors, and lack of general asymmetric catalytic systems, especially regarding the multicomponent variants. Herein, we reported a general copper‐Box system for asymmetric three‐component arylative radical cross‐coupling of vinylarenes and 1,3‐enynes, with oxime carbonates and aryl boronic acids. The reactions proceed under practical conditions in the absence or presence of visible‐light irradiation, affording chiral 1,1‐diarylalkanes, benzylic alkynes and allenes with good enantioselectivities. Mechanistic studies imply that the copper/Box complexes play a dual role in both radical generation and ensuing asymmetric cross‐coupling. In the cases of 1,3‐enynes, visible‐light irradiation could improve the activity of copper/Box complex toward the initial radical generation, enabling better efficiency match between radical formation and cross‐coupling.