  Celestial amplitudes which use conformal primary wavefunctions rather than
plane waves as external states offer a novel opportunity to study properties of
amplitudes with manifest conformal covariance and give insight into a potential
holographic celestial CFT at the null boundary of asymptotically flat space.
Since translation invariance is obscured in the conformal basis, features of
amplitudes that heavily rely on it appear to be lost. Among these are the
remarkable relations between gauge theory and gravity amplitudes known as the
double copy. Nevertheless, properties of amplitudes reflecting fundamental
aspects of the perturbative regime of quantum field theory are expected to
survive a change of basis. Here we show that there exists a well-defined
procedure for a celestial double copy. This requires a generalization of the
usual squaring of numerators which entails first promoting them to generalized
differential operators acting on external wavefunctions, and then squaring
them. We demonstrate this procedure for three and four point celestial
amplitudes, and give an argument for its validity to all multiplicities.
