When faced with real-world problems that seem unsolvable, humans display an exceptional degree of flexibility and creativity, improvising solutions with the limited resources available. In this essay, we propose a class of domain-independent AI challenge tasks -- MacGyver Problems -- that target these capabilities. We present a formal framework for generating these problems and outline a set of independent abilities that will let the research community make progress. We also consider, informally, ways in which researchers can measure progress and evaluate agents under the proposed framework.