  We reconsider the electrostatic contribution to the persistence length,
$\ell_e$, of a single, infinitely long charged polymer in the presence of
screening. A Gaussian variational method is employed, taking $\ell_e$ as the
only variational parameter. For weakly charged and flexible chains, crumpling
occurs at small length scales because conformational fluctuations overcome
electrostatic repulsion. The electrostatic persistence length depends on the
square of the screening length, $\ell_e\sim\kappa^{-2}$, as first argued by
Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to
a string of crumpled blobs. We compare our approach to previous theoretical
works (including variational formulations) and show that the result
$\ell_e\sim\kappa^{-1}$ found by several authors comes from the improper use of
a cutoff at small length scales. For highly charged and stiff chains, crumpling
does not occur; here we recover the OSF result and validate the perturbative
calculation for slightly bent rods.
