  Let P be a set of n points in general position in the plane. We study the
chromatic number of the intersection graph of the open triangles determined by
P. It is known that this chromatic number is at least n^3/27+O(n^2), and if P
is in convex position, the answer is n^3/24+O(n^2). We prove that for arbitrary
P, the chromatic number is at most n^3/19.259+O(n^2).
