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Strong damping-like spin-orbit torque (τDL) has great potential for enabling ultrafast energy-efficient magnetic memories, oscillators, and logic. So far, the reported τDL exerted on a thin-film magnet must result from an externally generated spin current or from an internal non-equilibrium spin polarization in noncentrosymmetric GaMnAs single crystals. Here, we for the first time demonstrate a very strong, unexpected τDL from current flow within ferromagnetic single layers of chemically disordered, face-centered-cubic CoPt. We establish that the novel τDL is a bulk effect, with the strength per unit current density increasing monotonically with the CoPt thickness, and is insensitive to the presence or absence of spin sinks at the CoPt surfaces. This τDL most likely arises from a net transverse spin polarization associated with a strong spin Hall effect (SHE), while there is no detectable long-range asymmetry in the material. These results broaden the scope of spin-orbitronics and provide a novel avenue for developing single-layer-based spin-torque memory, oscillator, and logic technologies.