  In two spatial dimensions, spin characterizes how particle states re-phase
under changes of frame that leave their momentum and energy invariant. Massless
particles can in principle have non-trivial spin in this sense, but all
existing field theories only describe the trivial case. This letter presents a
field theory for a massless particle with non-trivial physical spin. These
particles are the 2+1-dimensional analogues of "continuous-spin" particles in
3+1 dimensions, but here they have only two real degrees of freedom, related by
parity. They can be understood as massless generalizations of anyons, but are
simpler in key respects.
