  We numerically study an anyon chain based on the Haagerup fusion category,
and find evidence that it leads in the long-distance limit to a conformal field
theory whose central charge is $\sim 2$. Fusion categories generalize the
concept of finite group symmetries to non-invertible symmetry operations, and
the Haagerup fusion category is the simplest one which comes neither from
finite groups nor affine Lie algebras. As such, ours is the first example of
conformal field theories which have truly exotic generalized symmetries.
