Using the DØ detector, we have observed events produced in collisions that contain W or Z bosons in conjunction with very little energy deposition (“rapidity gaps”) in large forward regions of the detector. The fraction of W boson events with a rapidity gap (a signature for diffraction) is 0.89±0.190.17%, and the probability that the non-diffractive background fluctuated to yield the observed diffractive signal is 3×10−14, corresponding to a significance of 7.5 σ. The Z boson sample has a gap fraction of 1.44±0.610.52%, with a significance of 4.4 σ. The diffractive events have very similar properties to the more common non-diffractive component.