The recently discovered attractive force between hydrophobic surfaces is incorporated in a theory of polyelectrolyte solutions. Its influence on the second and third virial coefficients is estimated. Binary collisions between two polyions are virtually unaffected by attractive forces of long range whereas the impact on the third virial coefficient is enormous. The theoretical coefficients are compatible with those determined for solutions of rodlike xanthan by Kawakami and Norisuye. When the third virial coefficient is negative, the solution may become unstable. This instability appears to explain the onset of aggregation of DNA. The long-range attraction is strong enough to enforce stability of a hexagonal phase at low ionic strength. The predicted spacings agree with those found for tobacco mosaic virus by Millman et al.