The singular cohomology of the Grassmann variety of k-planes in n has a basis s ν indexed by partitions. The classical Pieri formula is an explicit rule for determining the coefficients in the expansion of the cup product
µ where 1 m is a column of length m and s 1 m is the mth Chern class of the tautological bundle. Lascoux and Schutzenberger [C. R. Acad. Sci. Paris 294 (1982), 447-450] formulated a generalization of Pieri's formula to the cohomology of the flag variety SL n /B and briefly indicated an algebraic proof. (Manivel [Cours Spécialisés 3 (1998)] provides details of this proof.) A geometric proof was given by Sottile [Ann. Inst. Fourier (Grenoble) 46 (1996), . In this paper we state and prove a generalization of this Pieri-type formula for the T -equivariant cohomology of the flag variety. We use the algebraic description of the T -equivariant cohomology of the flag variety due to Kostant and Kumar [Adv. Math. 62 (1986), 187-237] and Arabia [Bull. Soc. Math. France 117 (1989), 129-165], and our new formula exposes an equality of certain structure constants in this algebra. Our proof is an induction based on the original idea in Lascoux and Schützenberger.