We present an analytic theory for the structure of intrinsically flexible polyelectrolyte chains in solution at arbitrary concentrations, with or without added salt. We use a self-consistent approach based on an idea suggested by generalized Debye-Huckel theory, namely, that the screening length from polyions is wavevector-dependent, due to chain connectivity. At high wavevectors (short length scales), only counterions contribute to screening, but at lower wavevectors, both polyions and counterions contribute. The results of the theory are in quantitative agreement with molecular dynamics simulations, with no adjustable parameters.