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.
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