The density-matrix renormalization group method is used to study the ground
state of the two-chain zigzag-bond Hubbard model at quarter filling. We show
that, with a proper choice of the signs of hopping integrals, the ring exchange
mechanism yields ferromagnetic spin correlations between interchain neighboring
sites, and produces the attractive interaction between electrons as well as the
long-range pair correlations in the spin-triplet channel, thereby leading the
system to triplet superconductivity. We argue that this novel mechanism may
have possible relevance to observed superconductivity in Bechgaard salts