We propose a configuration interaction mechanism that leads to hole pairs with zero repulsion energy which are exact eigenstates of the two-band Hubbard Hamiltonian. The two-hole pairs have 1B2(xy) symmetry and arise from degenerate states at the Fermi level; we show that they must exist independently of the band filling. To discuss the possible relevance of these states to the problem of pairing in high-Tc superconductors we solve five- and nine-site model clusters with four holes. The quasiparticles become dressed by the interaction with the background holes and get paired with a set of valence band parameters well established for high-Tc cuprates. We predict a number of important experimental facts such as binding energies of the correct order of magnitude, the 1B1 (x2 - y2) symmetry of the order parameter and the singlet-triplet energy separation of the Cooper pairs.