[en] A novel universal (material-independent) negative differential resistance is shown to exist in strictly one-dimensional systems (quantum wires) as a consequence of energy and momentum conservation in the interaction of one-dimensional confined carriers with one-dimensional confined acoustic phonons. The average (steady state) carrier energy should also exhibit a non-monotonic dependence on the driving electric field. Candidate systems to exhibit this negative differential resistance are suspended semiconductor nanobridges and semiconducting carbon nanotubes