"In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime that is "closed", returning to its starting point."

Now, go to http://en.wikipedia.org/wiki/Virtual_particle#Vacuums and look at the picture "One-loop diagram with fermion propagator"

It seems to me that virtual particle pairs satisfy the CTC criterium.