  We show that there exist two 27 and one 27 bar of E6, net one D=4, N=1 chiral
matter supermultiplet as zero modes localized on the intersection of two
5-branes in the E8 x E8 heterotic string theory. The smeared intersecting
5-brane solution is used via the standard embedding to construct a heterotic
background, which provides, after a compactification of some of the transverse
dimensions, a five-dimensional Randall-Sundrum II like brane-world set-up in
heterotic string theory. As a by-product, we present a new proof of anomaly
cancellation between those from the chiral matter and the anomaly inflow onto
the brane without small instanton.
