A thin-film reflecting interference filter has been designed and constructed for the purpose of suppressing grating harmonics when monochromatizing synchrotron radiation. It consists of a layer of Si evaporated onto a substrate and makes use of interference between wave fronts reflected from the layer-substrate and vacuum-layer interfaces to suppress higher harmonics. The filter has proved useful over the fundamental wavelength range of 400-1200 A (~30-10 eV), maintaining a rejection ratio of fundamental to second harmonic exceeding 60. Calculations and measurements are presented, and the reflecting interference filter is compared with a critical-angle mirror used for the same purpose.