We present a local combinatorial formula for the Euler class of an n-dimensional PL spherical fiber bundle as a rational number eCH associated to a chain of n + 1 abstract subdivisions of abstract n-spherical PL cell complexes. The number eCH is a combinatorial (or matrix) Hodgetheoretic twisting cochain in Guy Hirsch’s homology model of the bundle associated with the PL combinatorics of the bundle.