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Strong room-temperature ferromagnetism is demonstrated in single crystalline Mn-doped ZnO thin films grown by molecular beam epitaxy. Very low Mn doping concentration is investigated, and the measured magnetic moment is much larger than what is expected for an isolated ion based on Hund's rules. The ferromagnetic behavior evolves with Mn concentration. Both magnetic anisotropy and anomalous Hall effect confirm the intrinsic nature of ferromagnetism. While the Mn dopant plays a crucial role, another entity in the system is needed to explain the observed large magnetic moments.