We use symmetry arguments combined with density functional theory to demonstrate that surfaces of centrosymmetric crystalline materials host surface phonons that are chiral. As model systems, we study slabs of highly symmetric AB rocksalt compounds, and find surface-localized phonons whose atomic displacements exhibit chiral motion. We further show that these chiral surface phonons generate in-plane magnetic moments at the surface. Our results indicate that chiral phonons can emerge in all crystalline materials as a result of reduced symmetry at surfaces or interfaces. These findings establish surfaces as a previously overlooked source of chiral phonons and their associated magnetic moments, which could play a role in surface-sensitive measurements.