The phase diagram of a bull; cholesteric liquid crystal in an electric or magnetic field applied perpendicular to the pitch axis is studied. This is an example of a system which exhibits different types of phase transitions between various modulated and homogeneous states. Possible transitions are of three types: (1) first order, (2) continuous and described as a condensation of solitons with repulsive interaction, or (3) continuous but characterized by a small order parameter. The detailed behavior of the temperature-field phase diagram is found to be strongly dependent on the intrinsic chirality, where the existence of an undulating state is predicted at high chirality. The relevant temperature, electric field, and chirality ranges are experimentally attainable.