Is it possible that the fundamental Planck constant has stochastic fluctuations? We entertain this possibility in this talk, motived by a possible quantum structure of spacetime. We describe in which sense Panck's constant is inconstant (a nontrivial affair for fundamental dimensionful quantities. In our schemeh is time dependent, given by random fluctuations around zero, characterized by the correlation time scale τ. As examples we briefly discuss possible experimental signatures using coherent states and interferometers.