We have studied the behavior of flexible polymer chains as they pass from a large diameter tube into a narrow capillary using the Brownian dynamics simulation technique. The polymer/solvent system studied was a very dilute solution of polystyrene in cyclohexane at a temperature of 35 degrees C. The polymer was modeled as a bead-spring chain, parameterized as to reproduce real polymer/solvent conditions. The end-to-end distance and the radius of gyration were seen to change abruptly as the chain entered the orifice of the capillary, giving rise to fracture of the polymer. In addition to chain fracture in the capillary orifice, chains were also observed to fracture within the capillary, and the fracture yield did not stabilize until a distance of about 0.3 cm into the capillary for an orifice diameter of 0.04 cm and the other instrumental dimensions and flow rates used in the study. We found that when the hydrodynamic interaction effect (HI) was not taken into consideration, the critical flow rate for fracture at the orifice showed a dependence on the molecular weight as Q(crit) similar to M(-1.8). This exponent is close to the theoretical value for breakage of fully extended chains. When HI was accounted for, the exponent was found to be significantly lower (-0.95), indicating chain fracture in a less extended conformation and showing that hydrodynamic interaction should not be disregarded in studies of polymer fracture in transient extensional flow.