  We set up a Batalin-Vilkovisky Quantum Master Equation for open-closed string
theory and show that the corresponding moduli spaces give rise to a solution, a
generating function for their fundamental chains. The equation encodes the
topological structure of the compactification of the moduli space of bordered
Riemann surfaces. The moduli spaces of bordered J-holomorphic curves are
expected to satisfy the same equation, and from this viewpoint, our paper
treats the case of the target space equal to a point. We also introduce the
notion of a symmetric Open-Closed Topological Conformal Field Theory and study
the L_\infty and A_\infty algebraic structures associated to it.
