The conformational space annealing (CSA) method is a powerful
global optimization method for sampling low-lying local minimum
energy conformations of a physical system. In this work, I apply
CSA to the study of a two-dimensional HP lattice model of a
protein, where a conformation is defined as a self-avoiding chain
on a lattice. I study the 36-residue chain with a particular
sequence HPHHPPHHPPPHHPHPPPHHPPHHPPPPHPHHPHPP presented
by Li et al., for which by exhaustive enumeration of compact conformations, 
only one such conformation with the lowest
energy was shown to exist. The CSA algorithm finds conformations
with energies lower than those found by Li et al. for 100
independent runs, demonstrating that the global minimum energy
conformation is not necessarily the most compact structure.