  We consider first order expressible properties of random perfect graphs. That
is, we pick a graph $G_n$ uniformly at random from all (labelled) perfect
graphs on $n$ vertices and consider the probability that it satisfies some
graph property that can be expressed in the first order language of graphs. We
show that there exists such a first order expressible property for which the
probability that $G_n$ satisfies it does not converge as $n\to\infty$.
