  We have carried out a theoretical analysis of the Landau-Ginzburg-Wilson
effective field theory of a classical incommensurate CDW in the presence of
weak quenched disorder. While the possibility a sharp phase transition and
long-range CDW order are precluded in such systems, we show that any discrete
symmetry breaking aspect of the charge order -- nematicity in the case of the
unidirectional (stripe) CDW we consider explicitly -- generically survives up
to a non-zero critical disorder strength. Such "vestigial order", which is
subject to unambiguous macroscopic detection, can serve as an avatar of what
would be CDW order in the ideal, zero disorder limit. Various recent
experiments in the pseudo-gap regime of the hole-doped cuprate high-temperature
superconductors are readily interpreted in light of these results.
