For observational purposes, gravity is often regarded classically, obeying Newton's law or Einstein's equations. Here I will show that, when the gravitational field is treated quantum-mechanically, the classical trajectories of falling objects are subject to random fluctuations ("noise"); intuitively, the fluctuations can be viewed as arising due to the bombardment of the falling objects by gravitons. Consequently, the classical geodesic deviation equation is replaced by a Langevin-like equation reminiscent of Brownian motion. The amplitude of the fluctuations depends on the quantum state of the gravitational field and can be greatly enhanced for certain classes of states. For such states, this fundamental noise might be observable at gravitational wave detectors and, if detected, would provide experimental evidence for the quantization of gravity and the existence of gravitons.