  A two chain ladder model is considered described by the strong coupling
$t-t^\prime-J-J^\prime$ Hamiltonian. For the case of two holes moving in a
background of antiferromagnetically interacting spins, exact, analytical
results are derived for the ground state energy and low-lying excitation
spectrum. The ground state is a bound state of two holes with total spin S=0.
The charge excitation is gapless and the spin excitation has a gap. The
corresponding wavefunctions are also exactly determined. The bound hole pair is
found to have symmetry of the d-wave type. In the limit of strong rung
coupling, the model maps onto an effective hard core boson model which exhibits
dominant superconducting pairing correlations.
