We report molecular dynamics simulations of a hydrophobic polymer-chain in aqueous solution between 260 K and 420 K at pressures of 1 bar, 3000 bar, and 4500 bar. The simulations reveal a hydrophobically collapsed state at low pressures and high temperatures. At 3000 bar and about 260 K and at 4500 bar and about 260 K, however, a transition to a swelled state is observed. The transition is driven by a smaller volume and a remarkably strong lower enthalpy of the swelled state, indicating a steep positive slope of the corresponding transition line. The swelling is stabilized almost completely by the energetically favorable state of water in the polymers hydrophobic first hydration shell at low temperatures. Although surprising, this finding is consistent with the observation of a positive heat capacity of hydrophobic solvation. Moreover, the slope and location of the observed swelling transition for the collapsed hydrophobic chain coincides remarkably well with the cold denaturation transition of proteins.