The ability to translate chemical cues into mechanical action is a defining feature of living organisms. Inspired to create materials that exhibit analogous ``life-like” behavior, we focus on chemically active two dimensional sheets which is driven by self-induced fluid flows. In contrast to active hard spheres, a two dimensional sheet is sufficiently flexible that the flowing fluid drives not only the propulsion, but also the shape evolution of the sheet, transforming the 2D layer into a moving, three dimensional object. Moreover, the transported, evolving sheet affects the flow of the surrounding fluid. Hence, chemically active materials of higher dimensionality and increased flexibility can exhibit rich, cooperative interactions.