We have studied the thermodynamics of isolated homopolymer chains of varying stiffness using a lattice model. A complex phase behaviour is found; phases include chain-folded "crystalline" structures. the disordered globule and the coil. It is found, in agreement with recent theoretical calculations, that the temperature at which the solid-globule transition occurs increases with chain stiffness, whilst the B-point has only a weak dependence on stiffness. Therefore, for sufficiently stiff chains there is no globular phase and the polymer passes directly from the solid to the coil. This effect is analogous to the disappearance of the liquid phase observed for simple atomic systems as the range of the potential is decreased.