We study the behavior of a hydrophobic chain near a hydrophobic boundary in two dimensions, adapting the decorated lattice model of Berkema and Widom (G.T. Barkema, B. Widom, J. Chem. Phys. 113, 2349 (2000)) to obtain effective, temperature-dependent intrachain and chain-boundary interactions. We use these interactions to construct two model Hamiltonians. The resulting partition functions may be integrated numerically. Our results compare favorably with preliminary Monte Carlo computations, using the same effective interactions. At relatively low temperatures and at high temperatures, we find that the chain is randomly configured in the ambient water, and detached from the wall, whereas at intermediate temperatures it adsorbs onto the wall in a stretched or partially folded state, again depending upon the temperature, and the energy of solvation.