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Cu₂IrO₃ is a new honeycomb iridate without thermodynamic signatures of long-range order. Here, we use muon spin relaxation to uncover the magnetic ground state of Cu₂IrO₃. We find a two-component depolarization with slow and fast relaxation rates corresponding to distinct regions with dynamic and static magnetism, respectively. X-ray absorption spectroscopy and first principles calculations identify a mixed copper valence as the origin of this behavior. Our results suggest that a minority of Cu²⁺ ions nucleate regions of static magnetism whereas the majority of Cu⁺/Ir⁴⁺ on the honeycomb lattice give rise to a Kitaev spin liquid.