Single-atom catalysts (SACs) consist of a low coverage of isolated metal atoms dispersed on a metal substrate, called single-atom alloys (SAAs), or alternatively single metal atoms coordinated to oxygen atoms on an oxide support. We present the synthesis of a new type of Co₁Cu SAC centers on a Cu₂O(111) support by means of a site-selective atomic layer deposition technique. Isolated metallic Co atoms selectively coordinate to the native oxygen vacancy sites (Cu sites) of the reconstructed Cu₂O(111) surface, forming a Co₁Cu SAA with no direct Co- O_x bonds. The centers, here referred to as Co₁Cu hybrid SACs, are found to stabilize the active Cu⁺ sites of the low-cost Cu₂O catalyst that otherwise is prone to deactivation under reaction conditions. The stability of the Cu₂O(111) surface was investigated by synchrotron radiation-based ambient-pressure X-ray photoelectron spectroscopy under reducing CO environment. The structure and reduction reaction are modeled by density functional theory calculations, in good agreement with experimental results.