We have studied the conformation change of a flexible linear polymer chain near the critical point of a binary liquid mixture using fluorescence correlation spectroscopy, which measured the hydrodynamic radius of the chains. Our results indicate that as the critical temperature (Tc) is approached, the chain size decreases. The polymer attains its most compact conformation when the correlation length of the critical fluctuations becomes comparable to the coil size. At very close to Tc, the polymer reexpands dramatically. To our knowledge, this is the first experimental evidence supporting the prediction of Brochard and de Gennes that a polymer chain will collapse and subsequently reswell on approaching Tc.