Shape-changing hydrogels that can bend, twist, or actuate in response to external stimuli are critical to soft robots, programmable matter, and smart medicine. Shape change in hydrogels has been induced by global cues, including temperature, light, or pH. Here we demonstrate that specific DNA molecules can induce 100-fold volumetric hydrogel expansion by successive extension of cross-links. We photopattern up to centimeter-sized gels containing multiple domains that undergo different shape changes in response to different DNA sequences. Experiments and simulations suggest a simple design rule for controlled shape change. Because DNA molecules can be coupled to molecular sensors, amplifiers, and logic circuits, this strategy introduces the possibility of building soft devices that respond to diverse biochemical inputs and autonomously implement chemical control programs.