  A \emph{co-bipartite chain} graph is a co-bipartite graph in which the
neighborhoods of the vertices in each clique can be linearly ordered with
respect to inclusion. It is known that the maximum cut problem (MaxCut) is
NP-Hard in co-bipartite graphs. We consider MaxCut in co-bipartite chain
graphs. We first consider the twin-free case and present an explicit solution.
We then show that MaxCut is polynomial time solvable in this graph class.
