A {\em string graph} is the intersection graph of a family of continuous arcs in the plane. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of {\em almost all} string graphs on n vertices can be partitioned into {\em five} cliques such that some pair of them is not connected by any edge (n→∞). As a corollary, we obtain that {\em almost all} string graphs on n vertices are intersection graphs of plane convex sets.