The diversity gains of cooperative relay networks are degraded in the presence of co-channel interference (CCI), which is the principal limiting factor in a properly planned cellular network. Optimum combining (OC) can be used to mitigate the adverse effects of CCI, which enables achieving diversity gains when CCI is present. The performance of OC in a channel state information (CSI) assisted amplify-and-forward (AF) relay network is analyzed when the destination node is affected by CCI, with the aid of a tight approximation for the signal-to-interference-plus-noise-ratio (SINR) at the destination node. Closed-form expressions are derived for the outage probability and the moment generating function for the approximated SINR. It is proved that OC results in a diversity gain of M, where M is the number of relay nodes. OC shows significant performance improvements over maximal-ratio combining (MRC), which reaches error floors at low-to-medium power levels.