The reported study of charge density waves at low temperatures is based on a microscopic theory. One feature of a charge density wave at low temperatures is a large shift in the chemical potential near its defects, such as solitons, dislocations, and pinning centers, which leads to a higher conductivity of material along chains when the charge density wave is immobile, and the wave dynamics is controlled by this shift. Equations describing the dynamics of a charge density wave have been derived and used to estimate the velocity of 2π-solitons along conducting chains. The resulting soliton mobility has proved to be low and makes a small contribution to the conductivity. The large shift in the chemical potential near strong pinning centers can lead to a considerable increase in linear conductivity along conducting chains.