<p>We construct the double copy of the chiral higher-spin theory. It is a Lorentz invariant theory with the little group spectrum given by the tensor square of the chiral higher-spin theory spectrum. Moreover, its interactions factorise in close analogy with the way interactions factorise in lower-spin double-copy theories. We also propose theories, which can be viewed as products of self-dual Yang-Mills theory, self-dual gravity and chiral higher-spin theories taken in different combinations and powers.</p>