  We construct an Euler system in the cohomology of the tensor product of the
Galois representations attached to two modular forms, using elements in the
higher Chow groups of products of modular curves. We use this Euler system to
prove a finiteness theorem for the strict Selmer group of the Galois
representation when the associated p-adic Rankin--Selberg L-function is
non-vanishing at s = 1.
