In various single-molecule experiments, a chiral polymer, such as DNA, is simultaneously pulled and twisted. We address an elementary but fundamental question raised by various authors: does the molecule overwind or unwind under tension? We show that within the context of the classic Kirchhoff-Love rod model of elastic filaments, both behaviors are possible, depending on the precise constitutive relations of the polymer. More generally, our analysis provides an effective linear response theory for helical structures that relates axial force and axial torque to axial translation and rotation. © 2013 American Physical Society.