When cooled to temperatures just a few billionths of a degree above absolute zero, dilute gases are governed by the principles of quantum mechanics. Because of the significant level of control and accessibility in these systems, they are powerful testbeds for theories of strongly interacting quantum materials, and wonderful platforms for discovering new phenomena. Ultracold polar molecules, for example, which can exhibit long-range electric dipole-dipole interactions, can be confined within a standing wave of light, known as an optical lattice, to simulate quantum magnetism in a crystalline solid, and to engineer exotic topological phases of matter. Here, we propose to develop a new experimental method of examining such a system, a molecular quantum gas microscope, which allows one to image individual molecules with single-lattice-site resolution. This would enable the direct observation of spatial structures and magnetic order, as well as time-resolved measurements of correlated spatial dynamics.