Control of collective properties of relativistic particles is increasingly important in modern accelerators. In particular, shot noise affects accelerator performance by driving instabilities or by competing with coherent processes. We present experimental observations of shot noise suppression in a relativistic beam at the Linac Coherent Light Source. By adjusting the dispersive strength of a chicane, we observe a decrease in the optical transition radiation emitted from a downstream foil. We show agreement between the experimental results, theoretical models, and 3D particle simulations. Show Partial Abstract