  A prism tableau is a set of reverse semistandard tableaux, each positioned
within an ambient grid. Prism tableaux were introduced to provide a formula for
the Schubert polynomials of A. Lascoux and M.P. Sch\"utzenberger. This formula
directly generalizes the well known expression for Schur polynomials as a sum
over semistandard tableaux. Alternating sign matrix varieties generalize the
matrix Schubert varieties of W. Fulton. We use prism tableaux to give a formula
for the multidegree of an alternating sign matrix variety.
