We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. The meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four-dimensional theory. Infinite chiral symmetry has far-reaching consequences for the spectral data, correlation functions, and central charges of any four-dimensional theory with ${\mathcal N}=2$ superconformal symmetry.Comment: 75 pages. v3: minor corrections. Final version -- published in Communications in Mathematical Physic

We engineer a large new set of four-dimensional N = 1 superconformal field theories by wrapping M5-branes on complex curves. We present new supersymmetric AdS 5 M-theory backgrounds which describe these fixed points at large N , and then directly construct the dual four-dimensional CFTs for a certain subset of these solutions. Additionally, we provide a direct check of the central charges of these theories by using the M5-brane anomaly polynomial. This is a companion paper which elaborates upon results reported in [1].