A strategy of relay catalysis by achiral borane and chiral phosphoric acid was successfully developed for the asymmetric hydrogenation of chromones, giving the desired products in high yields with up to 95% ee. Achiral borane and chiral phosphoric acid are highly compatible in this reaction. The achiral borane acts as a Lewis acid for the first-step hydrogenation, and the chiral phosphoric acid acts as an effective chiral proton shuttle to control the enantioselectivity.