Using a non-perturbative functional renormalization group approach involving both fermionic and bosonic fields we calculate the interaction-induced change of the Fermi surface of spinless fermions moving on two chains connected by weak interchain hopping t_{bot}. We show that interchain backscattering can strongly reduce the distance Delta between the Fermi momenta associated with the bonding and the antibonding band, corresponding to a large reduction of the effective interchain hopping t_{bot}^{*} A self-consistent one-loop approximation neglecting marginal vertex corrections and wave-function renormalizations predicts a confinement transition for sufficiently large interchain backscattering, where the renormalized t_{bot}^{*} vanishes. However, a more accurate calculation taking vertex corrections and wave-function renormalizations into account predicts only weak confinement in the sense that 0< | t_{bot}^{*} | << | t_{bot} |. Our method can be applied to other strong-coupling problems where the dominant scattering channel is known.
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