  Given a stochastic differential equation with path-dependent coefficients
driven by a multidimensional Wiener process, we show that the support of the
law of the solution is given by the image of the Cameron-Martin space under the
flow of mild solutions to a system of path-dependent ordinary differential
equations. Our result extends the Stroock-Varadhan support theorem for
diffusion processes to the case of stochastic differential equations with
path-dependent coefficients. The proof is based on functional Ito calculus.
