  We calculate the Landauer conductance through chaotic ballistic devices in
the semiclassical limit, to all orders in the inverse number of scattering
channels without and with a magnetic field. Families of pairs of
entrance-to-exit trajectories contribute, similarly to the pairs of periodic
orbits making up the small-time expansion of the spectral form factor of
chaotic dynamics. As a clue to the exact result we find that close
self-encounters slightly hinder the escape of trajectories into leads.
