Galileo famously established the principle of equivalence by dropping bodies of differing mass in the Earth's gravitational field. What if one considers quantum particles? Quantum mechanically, a particle can tunnel into the classically forbidden region of the gravitational potential, an effect that is explicitly mass dependent. Do quantum particles therefore violate the principle of equivalence? To investigate this, I consider an explicit model of a quantum clock to compute the expectation value of the time of flight of a particle in a background gravitational field, including the duration of tunneling. The calculation is not restricted to sharply-peaked wave packets, but may be applied to highly non-classical de-localized states, such as energy eigenstates. The results provide an intriguing insight into the deep consistency of physics, and suggest some interesting new experiments.