Described are the first examples of ketene–alkene [2+ 2] cycloadditions promoted by Lewis acids. Notable features of this method include (1) substantial rate acceleration relative to traditional thermal reactions,(2) good diastereoselectivities and yields for the formation of the cyclobutanone products, and (3) inverse diastereoselectivity compared with related thermal cycloadditions for many examples. These studies not only provide access to synthetically ...