Recent theories of bifurcation and chaos are used to analyze the dynamic behavior of the UNIPOL process for the production of polyethylene in the gas phase using the Ziegler-Natta catalyst. Dynamic behavior covers nide regions of the design and operating parameters domain of this industrially important unit. A conventional proportional-integral (PI) controller was implemented to stabilize the desired operating point on the unstable steady-state branch. The presence of the PI controller stabilized the desired unstable steady-state regions to a certain range of catalyst injection rate, by contrast, it is found out that the controlled process can go through a period doubling sequence leading to chaotic strange attractors. The practical implications of this analysis can be very serious, since chaos is shown to exist right near the desired operating point where high polyethylene production rates can be achieved.