Fulton's Universal Schubert polynomials represent general degeneracy loci for maps of vector bundles with rank conditions coming from a permutation. The Buch-Fulton Quiver formula expresses this polynomial as an integer linear combination of products of Schur polynomials in the differences of the bundles. We present a positive combinatorial formula for the coefficients. Our formula counts sequences of semi-standard Young tableaux satisfying certain conditions. One consequence is a reformulation of the quantization map of Fomin, Gelfand and Postnikov and Ciocan-Fontanine for partial flag manifolds. This is joint work with Anders Buch, Andrew Kresch and Harry Tamvakis.