  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 $X_H$.
