We have performed parallel tempering Monte Carlo simulations using a simple continuum heteropolymer model for proteins. All 10 heteropolymer sequences which we have studied have shown first-order transitions at low temperature to ordered states dominated by single chain conformations. These results are in contrast with the theoretical predictions of the random energy model for heteropolymers, from which we would expect continuous transitions to glassy behavior at low temperatures. (C) 2004 American Institute of Physics.