In ultraperipheral relativistic heavy-ion collisions, a photon from the electromagnetic field of one nucleus can fluctuate to a quark-antiquark pair and scatter from the other nucleus, emerging as a rho{0}. The rho{0} production occurs in two well-separated (median impact parameters of 20 and 40 F for the cases considered here) nuclei, so the system forms a two-source interferometer. At low transverse momenta, the two amplitudes interfere destructively, suppressing rho{0} production. Since the rho{0} decays before the production amplitudes from the two sources can overlap, the two-pion system can only be described with an entangled nonlocal wave function, and is thus an example of the Einstein-Podolsky-Rosen paradox. We observe this suppression in 200 GeV per nucleon-pair gold-gold collisions. The interference is 87%+/-5%(stat.)+/-8%(syst.) of the expected level. This translates into a limit on decoherence due to wave function collapse or other factors of 23% at the 90% confidence level.