The resonant tunneling phenomenon is well understood in quantum mechanics. I argue why a similar phenomenon must be present in quantum field theory. Using the functional Schr\"odinger method I show how resonant tunneling through multiple barriers takes place in quantum field theory with a single scalar field. I also show how this phenomenon in scalar quantum field theory can lead to an exponential enhancement of the single-barrier tunneling rate. My analysis is carried out in the thin-wall approximation.  I discuss a possible explanation of the fast nucleation of the B phase of superfluid Helium-3 as an application.