Human DNA polymerase eta (Pol eta) plays an essential protective role against skin cancer caused by cyclobutane thymine-thymine dimers (TTDs), a frequent form of DNA damage arising from exposure to the sun. This enzyme rescues stalled replication forks at the TTDs by inserting bases opposite these DNA defects. Herein we calculate binding free energies for a free deoxyribose nucleotide triphosphate, dATP or dGTP, to Pol eta complexed with undamaged or damaged DNA. The calculations indicate that the binding of dATP to the enzyme-DNA complex is thermodynamically favored for TTD-containing DNA over undamaged DNA, most likely because of more extensive hydrogen-bonding interactions between the TTD and the enzyme that hold the TTD more rigidly in place. The calculations also illustrate that dATP binding is thermodynamically favored over dGTP binding at both thymine positions of the TTD, most likely due to more persistent and stable hydrogen-bonding interactions between the TTD and dATP than between the TTD and dGTP. This free energy difference is slightly greater for binding at the 5' thymine position than at the 3' thymine position, presumably because of stabilization arising from the A:T base pair formed at the 3' position of the TTD in the previous step of Pol eta function. All of these trends in binding free energies are consistent with experimental measurements of binding strength, fidelity, processivity, and overall efficiency. The insights gained from this analysis have implications for drug design efforts aimed at modifying the binding properties of this enzyme for improving cancer chemotherapy treatments.