High-entropy alloys (HEAs) have attracted extensive research interest for their outstanding mechanical, electrochemical, and magnetic properties due to the highly random occupation of near equimolar multi-principal elements. The functionalities are severely influenced by the highly disordered lattice structure at grain boundaries and random orientation of grains in polycrystalline samples. Here, epitaxial CrMnFeCoNi HEA thin films of (001) orientation are prepared by laser-assisted molecular beam epitaxy on MgO substrates using a Cu buffer layer. A spontaneous exchange bias (SEB) effect is observed in a 98 nm thick CrMnFeCoNi HEA thin film. The SEB effect is related to a newly formed ferromagnetic (FM)/spin glass (SG) interface generated by field-induced irreversible growth of FM regions. The interfacial spins of SG domains are gradually consumed during the initial magnetizing process, leading to the consequent reservation of unidirectional anisotropy. The observation of SEB in HEA films expands their functions, which may be applied in novel magnetic devices.