Self-avoiding walks on a three-dimensional (3D) simple cubic lattice are often used to model polymers, especially proteins. The Hamiltonian is generally taken to be a function of contacts between sequentially nonadjacent residues. The set of all conformations having a particular set of contacts occupies the same energy level, and one would like to estimate the degeneracy or chain entropy of the level. Degeneracies observed in an exhaustive enumeration of short chain configurations are fitted to simple empirical formulas depending on the length of the chain, the number of contacts, and statistics related to the particular set of contacts.