The ability to measure tiny variations in the local gravitational acceleration allows, besides other applications, the detection of hidden hydrocarbon reserves, magma build-up before volcanic eruptions, and subterranean tunnels. Several technologies are available that achieve the sensitivities required for such applications (tens of microgal per hertz(1/2)): free-fall gravimeters, spring-based gravimeters, superconducting gravimeters, and atom interferometers. All of these devices can observe the Earth tides: the elastic deformation of the Earth's crust as a result of tidal forces. This is a universally predictable gravitational signal that requires both high sensitivity and high stability over timescales of several days to measure. All present gravimeters, however, have limitations of high cost (more than 100,000 US dollars) and high mass (more than 8 kilograms). Here we present a microelectromechanical system (MEMS) device with a sensitivity of 40 microgal per hertz(1/2) only a few cubic centimetres in size. We use it to measure the Earth tides, revealing the long-term stability of our instrument compared to any other MEMS device. MEMS accelerometers--found in most smart phones--can be mass-produced remarkably cheaply, but none are stable enough to be called a gravimeter. Our device has thus made the transition from accelerometer to gravimeter. The small size and low cost of this MEMS gravimeter suggests many applications in gravity mapping. For example, it could be mounted on a drone instead of low-flying aircraft for distributed land surveying and exploration, deployed to monitor volcanoes, or built into multi-pixel density-contrast imaging arrays.