  Four-dimensional N=2 superconformal field theories have families of protected
correlation functions that possess the structure of two-dimensional chiral
algebras. In this paper, we explore the chiral algebras that arise in this
manner in the context of theories of class S. The class S duality web implies
nontrivial associativity properties for the corresponding chiral algebras, the
structure of which is best summarized in the language of generalized
topological quantum field theory. We make a number of conjectures regarding the
chiral algebras associated to various strongly coupled fixed points.
