We study the quantum nonlinear response to an applied electric field E of a one-dimensional pinned charge-density wave or Luttinger liquid in the presence of disorder. From an explicit construction of low-lying metastable states and of bounce instanton solutions between them, we demonstrate quantum creep v=e−c/E1/2 as well as a sharp crossover at E=E∗ towards a linear response form consistent with variable-range hopping arguments, but dependent only on electronic degrees of freedom.