Chromatic Symmetric Functions of Hypertrees

The chromatic symmetric function X-H of a hypergraph H is the generating function for all colorings of H so that no edge is monochromatic. When H is an ordinary graph, it is known that X-H is positive in the fundamental quasisymmetric functions F-S, but this is not the case for general hypergraphs. We exhibit a class of hypergraphs H-hypertrees with prime-sized edges for which X-H is F-positive, and give an explicit combinatorial interpretation for the F-coefficients of X-H.