We extend the results found for Matrix String Theory to Heterotic Matrix String Theory, i.e. to a 2d O(N) SYM theory with chiral (anomaly free) matter and N=(8,0) supersymmetry. We write down the instanton equations for this theory and solve them explicitly. The solutions are characterized by branched coverings of the basis cylinder, i.e. by compact Riemann surfaces with punctures. We show that in the strong coupling limit the action becomes the heterotic string action plus a free Maxwell

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... . Moreover the amplitude based on a Riemann surface with p punctures and h handles is proportional to g^2-2h-p, as expected for the heterotic string interaction theory with string coupling g_s=1/g.