The performance of optimum combining (OC) used in a decode-and-forward relay network over Nakagami-m fading channels in the presence of co-channel interference at the relay nodes and at the destination is analyzed. A closed-form expression is derived for the exact outage probability. It is found that OC cannot be used to achieve end-to-end diversity gain when interference is present at single-antenna relays, but the outage probability floor at the destination receiver is lowered by the OC. If the interference is present only at the destination, diversity gains can be achieved using OC. The performance of OC is compared with maximal-ratio combining (MRC) and OC achieves diversity gain if interference is present only at the destination node, whereas MRC does not.