The theory of relativity provides a consistent frame-independent classical description of nature. A case in point is the classical equivalence principle, which bridges the notions of inertial and gravitational mass. Of unique importance is the free-falling frame which is defined by the gravitational acceleration. In the quantum domain the equivalence principle involves a gauge phase that is observable if the wave function – the fundamental tenet of quantum theory – allows an object to interfere with itself after being simultaneously at rest in two different frames. Here we observe this phase of a superposition of an object at rest in two fundamental frames – the inertial frame and the free-fall frame, also referred to as the Newtonian and Einsteinian frames. We do so with a unique cold-atom interferometer in which one of the wave packets stays static in the lab frame while the other is in free-fall. Our observation is yet another fundamental test of the interface between quantum theory and gravity. The new interferometer also opens the door for further probing of the latter interface, as well as to novel searches for exotic physics.