  Several active galactic nuclei (AGN) with multiple sets of emission lines
separated by over 2000 km/s have been observed recently. These have been
interpreted as being due to massive black hole (MBH) recoil following a black
hole merger, MBH binaries, or chance superpositions of AGN in galaxy clusters.
Moreover, a number of double-peaked AGN with velocity offsets of ~ a few 100
km/s have also been detected and interpreted as being due to the internal
kinematics of the narrow line regions or MBH binary systems. Here we reexamine
the superposition model. Using the Millennium Run we estimate the total number
of detectable AGN pairs as a function of the emission line offset. We show that
AGN pairs with high velocity line separations up to ~2000 km/s are very likely
to be chance superpositions of two AGN in clusters of galaxies for reasonable
assumptions about the relative fraction of AGN. No superimposed AGN pairs are
predicted for velocity offsets in excess of ~3000 km/s as the required AGN
fractions would violate observational constraints. The high velocity AGN pair
numbers predicted here are competitive with those predicted from the models
relying on MBH recoil or MBH binaries. However, the model fails to account for
the largest emission line velocity offsets that require the presence of MBH
binaries.
