A comparison of the osmotic coefficient of a synthetic stiff-chain polyelectrolyte with the prediction of the Poisson-Boltzmann (PB) cell model is presented. The polyelectrolyte consists of a poly(p-phenylene) backbone with attached cationic groups (charge parameter 3.4) and either chloride or iodine counterions. The osmotic coefficient phi was deduced from the osmotic pressure measured from dilute solutions (0.05-3.6 g/L) without added salt. The data demonstrate that the PB cell model captures the essential features of the experimental results without adjustable parameters. It fails to give a quantitative description, however, because the experimental phi is significantly smaller than the value predicted by the PB cell model. Possible reasons for this discrepancy as the neglect of the ion-ion correlations or specific interactions between the macroion and the counterions in the PB cell model are discussed.