  There has been recent interest in the question of whether QCD collinear
singularities can be viewed as the OPE of a two-dimensional CFT. We analyze a
version of this question for the self-dual limit of pure gauge theory
(incorporating states of both helicities). We show that the known one-loop
collinear singulaties do not form an associative chiral algebra. The failure of
associativity can be traced to a novel gauge anomaly on twistor space. We find
that associativity can be restored for certain gauge groups if we introduce an
unusual axion, which cancels the twistor space anomaly by a Green-Schwarz
mechanism. Alternatively, associativity can be restored for some gauge groups
with carefully chosen matter.
