  We study the constraints imposed by the existence of a single higher spin
conserved current on a three dimensional conformal field theory. A single
higher spin conserved current implies the existence of an infinite number of
higher spin conserved currents. The correlation functions of the stress tensor
and the conserved currents are then shown to be equal to those of a free field
theory. Namely a theory of N free bosons or free fermions. This is an extension
of the Coleman-Mandula theorem to CFT's, which do not have a conventional S
matrix. We also briefly discuss the case where the higher spin symmetries are
"slightly" broken.
