Disorder, prevalent in nature, is intimately involved in such spectacular effects as the fractional quantum Hall effect and vortex pinning in type-II superconductors. Understanding the role of disorder is therefore of fundamental interest to materials research and condensed matter physics. Universal behavior, such as Anderson localization, in disordered non-interacting systems is well understood. But, the effects of disorder combined with strong interactions remains an outstanding challenge to theory. Here, we experimentally probe a paradigm for disordered, strongly-correlated bosonic systems-the disordered Bose-Hubbard (DBH) model-using a Bose-Einstein condensate (BEC) of ultra-cold atoms trapped in a completely characterized disordered optical lattice. We determine that disorder suppresses condensate fraction for superfluid (SF) or coexisting SF and Mott insulator (MI) phases by independently varying the disorder strength and the ratio of tunneling to interaction energy. In the future, these results can constrain theories of the DBH model and be extended to study disorder for strongly-correlated fermionic particles. Comment: 15 pages, 4 figures updated to correct errors in referencing previous work