In a two dimensional Monte Carlo simulation of the coil-to-globule transition of a homopolymer chain, we observed a state between the coil and globule states, in which the center of the chain has a higher density than the periphery. The existence of this special state indicates that the melting of the globule is not an all-or-none process, i.e., the periphery melts prior to the center. This state resembles the molten globule state of a protein chain and confirms the previous experimental results.