  We consider M-theory in the presence of M parallel M5-branes probing a
transverse A_{N-1} singularity. This leads to a superconformal theory with
(1,0) supersymmetry in six dimensions. We compute the supersymmetric partition
function of this theory on a two-torus, with arbitrary supersymmetry preserving
twists, using the topological vertex formalism. Alternatively, we show that
this can also be obtained by computing the elliptic genus of an orbifold of
recently studied M-strings. The resulting 2d theory is a (4,0) supersymmetric
quiver gauge theory whose Higgs branch corresponds to strings propagating on
the moduli space of SU(N)^{M-1} instantons on R^4 where the right-moving
fermions are coupled to a particular bundle.
