  We give a Pieri rule for the torus-equivariant cohomology of (submaximal)
Grassmannians of Lie types B, C, and D. To the authors' best knowledge, our
rule is the first manifestly positive formula, beyond the equivariant Chevalley
formula. We also give a simple proof of the equivariant Pieri rule for the
ordinary (type A) Grassmannian.
