Observations of d-band quantum well states are made for atomically uniform Ag films on Fe(100) using angle-resolved photoemission. For increasing film thicknesses, quantum well peaks within the small 4d bandwidth multiply rapidly and merge into a bulklike spectrum at approximately 25 monolayers. An analysis of the peak positions yields a highly accurate bulk band structure of Ag. A very narrow d-band peak width (13 meV) is observed at the band top.