  The work of Mills, Robbins, and Rumsey on cyclically symmetric plane
partitions yields a simple product formula for the number of lozenge tilings of
a regular hexagon, which are invariant under roation by $120^{\circ}$. In this
paper we generalize this result by enumerating the cyclically symmetric lozenge
tilings of a hexagon in which four triangles have been removed in the center.
