An understanding of the various states available to a polypeptide chain is important for a description of the protein folding process. We use a 16-monomer chain on a two-dimensional square lattice to model a protein. This makes it possible to enumerate all self-avoiding conformations from which any equilibrium thermodynamic quantity can be calculated. By varying the external conditions of temperature and average attraction, we construct a phase diagram for the model protein. It is found to have an extended coil state, a homopolymer-like disorganized globule state, and an organized frozen globule state that corresponds to the lowest energy (native) conformation. The exact model results agree well with analytical heteropolymer theory.