We report the existence of a localization-delocalization transition in the classical plasma modes of a one-dimensional Wigner crystal with a white-noise potential environment at T=0. Finite-size scaling analysis reveals a divergence of the localization length at a critical eigenfrequency. Further scaling analysis indicates power law behavior of the critical frequency in terms of the relative interaction strength of the charges. A heuristic argument for this scaling behavior is consistent with the numerical results. Additionally, we explore a particular realization of random-bond disorder in a one-dimensional Wigner lattice in which all of the collective modes are observed to be localized.