  In ultra-peripheral 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
fermi for the cases considered here) nuclei, so the system forms a 2-source
interferometer. At low transverse momenta, the two amplitudes interfere
destructively, suppressing $\rho^0$ production. Since the $\rho^0$ decay before
the production amplitudes from the two sources can overlap, the two-pion system
can only be described with an entangled non-local 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 $87% \pm 5%
{\rm (stat.)}\pm 8%$ (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.
