  We study the interplay between an on-site Hubbard repulsion and quasiperiodic
potential in one-dimensional fermion chains using the density matrix
renormalization group. We find that, at half-filling, the quasiperiodic
potential can destroy the Mott gap, leading to a metallic Luttinger liquid
phase between the gapped Mott insulator at strong repulsion and localized
gapless Aubry- Andr\'e insulator at strong quasiperiodic potential. Away from
half-filing, the metallic phase of the interacting model persists to larger
critical strengths of the potential than in the non-interacting case,
suggesting interaction-stabilized delocalization at finite doping. We
characterize the Luttinger liquid through its charge and spin correlations,
structure factors, and entanglement entropy.
