I will explain how to axiomatize the notion of a chiral WZW
model using the formalism of vertex operator algebras. This class of
models is in almost bijective correspondence with pairs (G,k), where G
is a connected (not necessarily simply connected) Lie group and k in
H^4(BG,Z) is a degree four cohomology class subject to a certain
positivity condition. To my surprise, I have found a couple extra
models which satisfy all the defining properties of chiral WZW models,
but which don't come from pairs (G,k) as above. The simplest such
model is related to the Lie group E8 x E8.