  We investigate superconformal surface defects in four-dimensional N=2
superconformal theories. Each such defect gives rise to a module of the
associated chiral algebra and the surface defect Schur index is the character
of this module. Various natural chiral algebra operations such as
Drinfeld-Sokolov reduction and spectral flow can be interpreted as
constructions involving four-dimensional surface defects. We compute the index
of these defects in the free hypermultiplet theory and Argyres-Douglas
theories, using both infrared techniques involving BPS states, as well as
renormalization group flows onto Higgs branches. In each case we find perfect
agreement with the predicted characters.
