The first synthesis of hebelophyllene E is presented, along with assignment of its previously unknown relative configuration through synthesis of epi-ent-hebelophyllene E. Development of a catalytic enantioselective [2+2] cycloaddition of alkenes and allenoates provides access to the required chiral geminal dimethylcyclobutanes. Key to its success is the identification of a novel oxazaborolidine catalyst which promotes the cycloaddition in high enantioselectivities with good functional-group tolerance (9 examples, up to 97:3 e.r.). Thus, a late-stage cycloaddition using a fully functionalized alkene, followed by a diastereoselective reduction allows a concise entry to this class of natural products.