In this paper, we initiate the study of the protein folding problem from an integer linear programming perspective. The particular variant of protein folding that we examine is known as the hydrophobic-hydrophilic (HP) model of protein folding on the integer lattice. This problem is known to be NP-hard and also maxSNP-hard. We examine various alternate formulations for the planar version of this problem and present some preliminary computational results. Hopefully, this sets the stage for a polyhedral combinatorics assault on this important problem.