  The chiral algebra of a 4D $N\geq2$ superconformal field theory is a vertex
operator algebra generated by the Schur subsector of the 4D theory and its
rigid (yet rich) structure has been useful in constraining and classifying 4D
N=2 SCFTs. We study how the chiral algebra arises from the worldsheet
perspective. In the worldsheet CFT dual of 4D N=4 SYM at the free point, we
extract the subsector that corresponds to the spacetime Schur operators at
generic coupling, and show how they generate the chiral algebra. The result can
be easily generalized to 4D N=2 superconformal field theories that arise as
orbifolds of 4D N=4 SYM.
