Self-diffusion coefficients of polyelectrolyte chains in aqueous semidilute salt-free solutions of sodium poly(styrenesulfonate) have been determined at room temperature as a function of the concentration and the molar mass by use of pulsed field gradient NMR. Self-diffusion coefficients were found to be inversely proportional to the molar mass for degrees of polymerization up to about 1000. The result is discussed in terms of a polymer melt analogy amounting to local friction and ineffectiveness of entanglements. The observation of molar mass independent crossover behavior of D(s) as a function of the concentration is in line with this interpretation. Comparison with results from literature leads to the conclusion that this crossover is a general feature of low-salt polyelectrolyte solutions. It is tentatively identified with the Odijk c** crossover where the chain persistence length equals the transient network mesh size.