  We argue that negative critical currents arise generically in Josephson
junctions formed by single channel conductors. Specifically, we theoretically
study the Josephson coupling between two superconducting leads connected by a
one-dimensional conductor in the Coulomb blockade regime. We show that in the
clean regime the sign of the critical current alternates with the number of
electrons in the normal region. For odd occupancy the critical current is
negative even when the number of electrons on the conductor is large.
