An unexpected size hysteresis effect was observed in the globule-to-coil transition of poly(N-isopropylacrylamide) attached to surfaces of latex particles. The magnitude of the effect was found to be critically dependent upon the period for which the polymer was incubated in the globular form and upon the temperature of incubation. Hysteresis was attributed to the physical formation of knots when the globular chains swelled rapidly during their transformation into coils. These knots were associated with topological entanglements that were formed in the globular state and that had insufficient time to disentangle in the rapid globule-to-coil transition. A simple theory was developed that permitted the rate coefficients for the formation of entanglements that led to knotting to be evaluated, along with the activation energy for the process.