We report inelastic neutron scattering measurements of the phonon density of states in Mg 11B2, which has a superconducting transition at 39.2 K. The acoustic phonons extend in energy to 36 meV, and there are highly dispersive optic branches peaking at 54, 78, 89, and 97 meV. A simple Born-von Kàrmàn model reproduces the mode energies, and provides an estimate of the electron-phonon coupling of lambda approximately 0.9. Furthermore, the estimated boron and magnesium contributions to the isotope effect are in qualitative agreement with experiment. The data confirm that a conventional phonon mechanism, with moderately strong electron-phonon coupling, can explain the observed superconductivity.