Sampling of various types of acyclic orientations of chordal graphs plays a central role in several AI applications. In this work we investigate the use of the recently proposed general partial rejection sampling technique of Guo, Jerrum, and Liu, based on the Lovasz Local Lemma, for sampling partial acyclic orientations. For a given undirected graph, an acyclic orientation is an assignment of directions to all of its edges so that there is no directed cycle. In partial orientations some edges are allowed to be undirected. We show how the technique can be used to sample partial acyclic orientations of chordal graphs fast and with a clearly specified underlying distribution. This is in contrast to other samplers of various acyclic orientations with running times exponentially dependent on the maximum degree of the graph.