  A graph is unichord free if it does not contain a cycle with exactly one
chord as its subgraph. In [3], it is shown that a graph is unichord free if and
only if every minimal vertex separator is a stable set. In this paper, we first
show that such a graph can be recognized in polynomial time. Further, we show
that the chromatic number of unichord free graphs is one of (2,3, \omega(G)).
We also present a polynomial-time algorithm to produce a coloring with
\omega(G) colors.
