  To any generic curve in an oriented surface there corresponds an oriented
chord diagram, and any oriented chord diagram may be realized by a curve in
some oriented surface. The genus of an oriented chord diagram is the minimal
genus of an oriented surface in which it may be realized. Let g_n denote the
expected genus of a randomly chosen oriented chord diagram of order n. We show
that g_n satisfies: g_n = n/2 - Theta(ln n).
