Coherent coupling between single quantum objects is at the very heart of modern quantum physics. When the coupling is strong enough to prevail over decoherence, it can be used to engineer quantum entangled states. Entangled states have attracted widespread attention because of applications to quantum computing and long-distance quantum communication. For such applications, solid-state hosts are preferred for scalability reasons, and spins are the preferred quantum system in solids because they offer long coherence times. Here we show that a single pair of strongly coupled spins in diamond, associated with a nitrogen-vacancy defect and a nitrogen atom, respectively, can be optically initialized and read out at room temperature. To effect this strong coupling, close proximity of the two spins is required, but large distances from other spins are needed to avoid deleterious decoherence. These requirements were reconciled by implanting molecular nitrogen into high-purity diamond.