Abstract
A new theory of a polyelectrolyte solution at low densities is proposed. It is shown that below temperature Tcl, counterions associate with polyions forming clusters consisting of a polyion and of n counterions. The distribution of cluster sizes is Gaussian, and leads to a strong logarithmic correction to the limiting laws obtained by Manning. Above Tcl the limiting laws remain unchanged. Furthermore, unlike some recent suggestions it is demonstrated that counterion condensation is distinct from the Kosterlitz-Thouless phase transition.