A class of special Lagrangian subspaces of Calabi-Yau manifolds is considered and their mirrors, certain holomorphic varieties of the mirror geometry, are identified. This transforms the counting of holomorphic disc instantons ending on the Lagrangian submanifold to the classical Abel-Jacob map on the mirror. We discuss flat coordinates on the moduli spaces, and a certain quantum ambiguity which influences disc counting. Highly non-trivial new predictions for disc counting are obtained.