Recent advances in atom interferometry have led to the development of quantum inertial sensors with outstanding performance in terms of sensitivity, accuracy, and long-term stability. For ground-based implementations, these sensors are ultimately limited by the free-fall height of atomic fountains required to interrogate the atoms over extended timescales. This limitation can be overcome in Space and in unique ``microgravity'' facilities such as drop towers or free-falling aircraft. These facilities require large investments, long development times, and place stringent constraints on instruments that further limit their widespread use. The available ``up time'' for experiments is also quite low, making extended studies challenging. In this work, we present a new approach in which atom interferometry is performed in a laboratory-scale Einstein Elevator. Our experiment is mounted to a moving platform that mimics the vertical free-fall trajectory every 13.5 seconds. With a total interrogation time of $2T = 200$ ms, we demonstrate an acceleration sensitivity of $6 \times 10^{-7}$ m/s$^{2}$ per shot, limited primarily by the temperature of our atomic samples. We further demonstrate the capability to perform long-term statistical studies by operating the Einstein Elevator over several days with high reproducibility. These represent state-of-the-art results achieved in microgravity and further demonstrates the potential of quantum inertial sensors in Space. Our microgravity platform is both an alternative to large atomic fountains and a versatile facility to prepare future Space missions.