In this paper we extend our recent approach to the collapse or random AB copolymers [F. Ganazzoli, J. Chem. Phys. 108, 9924 (1998)] to amphiphilic chains. These copolymers are formed by unlike units having varying degrees of solvophilicity and solvophobicity (or polarity and hydrophobicity if the solvent is water) and model the behavior of globular proteins. The equilibrium state is found by self-consistent minimization of the intramolecular free energy, which includes two-body interactions, either attractive or repulsive depending on the interacting units, three-body and screened repulsive interactions among all the units, and configurational entropy. Chain connectivity is accounted for throughout. We consider a fixed sequence of units along the chain, which does not give rise to any entropy of mixing. In keeping with our earlier results, we find that amphiphilic copolymers form monomolecular micelles with a compact core formed by the hydrophobic units and a looser outer corona with the polar units. Different metastable states are also present, either with a few isolated hydrophobic units in the outer region, or with two distinct globular cores. In the latter case, the coalescence of the cores is prevented by their polar periphery. A notable feature is that the multiplicity of metastable states, and sometimes also of the stable ones, is often significantly larger than in AB copolymers. Advantages and shortcomings of the procedure in connection also with other theoretical studies of protein folding are briefly discussed.