The classical theory of the electrostatic persistence length of polyel
ectrolyte chains due to Odijk, Skolnick and Fixman (OSF) is revisited.
In contrast to the original theory, our approach takes into account t
he effect of fluctuations in the chain configuration. As a result, we
find that the OSF theory, although correct for intrinsically rigid pol
yelectrolytes, breaks down for flexible chains. A quantitative criteri
on is established to distinguish between flexible and rigid chains. Fo
r flexible chains, we use a variational theory to compute the electros
tatic persistence length, which is found to be proportional to the Deb
ye-Huckel screening length, in agreement with many experimental and si
mulation results.