Vibrational spectroscopy and helium nanodroplet isolation are used to determine the gas-phase thermochemistry for isomerization between conformations of the model dipeptide, N-acetylglycine methylamide (NAGMA). A two-stage oven source is implemented to produce a gas-phase equilibrium distribution of NAGMA conformers, which is preserved when individual molecules are captured and cooled to 0.4 K by He nanodroplets. With polarization spectroscopy, the IR spectrum in the NH stretch region is assigned to a mixture of two conformers having intramolecular hydrogen bonds composed of either five- or seven-membered rings, C-5 and C-7, respectively. The C-5 to C-7 interconversion enthalpy and entropy, obtained from a van't Hoff analysis, are -4.52 +/- 0.12 kJ/mol and -12.4 +/- 0.2 J/(mol.K), respectively. The experimental thermochemistry is compared to high-level electronic structure theory computations.