  An outerstring graph is an intersection graph of curves that lie in a common
half-plane and have one endpoint on the boundary of that half-plane. We prove
that the class of outerstring graphs is $\chi$-bounded, which means that their
chromatic number is bounded by a function of their clique number. This
generalizes a series of previous results on $\chi$-boundedness of outerstring
graphs with various additional restrictions on the shape of curves or the
number of times the pairs of curves can cross. The assumption that each curve
has an endpoint on the boundary of the half-plane is justified by the known
fact that triangle-free intersection graphs of straight-line segments can have
arbitrarily large chromatic number.
