We show that a 2D CFT consisting of a central charge c Liouville theory, a chiral level one, rank N Kac-Moody algebra and a weight −3/2 free fermion holographically generates 4D MHV leaf amplitudes associated to a single hyperbolic slice of flat space. Celestial amplitudes arise in a large-N and semiclassical large-c limit, according to the holographic dictionary, as a translationally-invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact AdS3 Witten diagrams.