Traditional classifications of crystalline phases focus on nuclear degrees of freedom. Through the examination of both electronic and nuclear structure, we introduce the concept of an electronic plastic crystal. Such a material is classified by crystalline nuclear structure, while localized electronic degrees of freedom-here lone pairs-exhibit orientational motion at finite temperatures. This orientational motion is an emergent phenomenon arising from the coupling between electronic structure and polarization fluctuations generated by collective motions, such as phonons. Using ab initio molecular dynamics simulations, we predict the existence of electronic plastic crystal motion in halogen crystals and halide perovskites, and suggest that such motion may be found in a broad range of solids with lone pair electrons. Such fluctuations in the charge density should be observable, in principle, via synchrotron scattering.