The persistence length of a single, strongly charged, stiff polyelectrolyte chain is investigated theoretically. Path integral formulation is used to obtain the effective electrostatic interaction between the monomers. We find significant deviations from the classical Odijk, Skolnick and Fixman (OSF) result. An induced attraction between monomers is due to thermal fluctuations and correlations between bound counterions. The electrostatic persistence length is found to be smaller than the OSF value and indicates a possible mechanical instability (collapse) for highly charged polyelectrolytes with multivalent counterions. In addition, we calculate the amount of condensed counterions on a slightly bent polyelectrolyte. More counterions are found to be adsorbed as compared to the Manning condensation on a cylinder.