We construct an extended-Lagrangian Brownian dynamics algorithm for charged polymers in simple electrolyte solutions which explicitly couples fluctuations in polyion conformation to charge density fluctuations in the ion atmosphere without explicit simulation of solvent and counterions. The algorithm is applicable in the Debye-Huckel limit of low solvent ionic strength. The theoretical description of the system has the appearance of conventional linearized Poisson-Boltzmann theory, except that the screening lengths become space- and time-dependent, hence we consider the algorithm a "dynamic" extension of linearized Poisson-Boltzmann theory. Use of the algorithm is illustrated in a simple model system, and some polyion properties are compared to exact results obtained by conventional Brownian dynamics simulation. (C) 2001 American Institute of Physics.