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The magnetic moment of the chiral phonon in transition metal dichalcogenides (TMDCs) holds promise for valleytronic and spintronic applications. As the TMDC lattice is achiral, an important question is how to lift the degeneracy of the chiral phonon. In this work, we study the monolayer iron-doped molybdenum disulfide (Fe:MoS₂) grown via chemical vapor deposition. Our magnetometry measurements demonstrate that Fe:MoS₂ is ferromagnetic at room temperature. Helicity-resolved Raman spectroscopy shows that at zero external magnetic field the chiral phonon in Fe:MoS₂ splits into two modes due to the lifted time-reversal symmetry.  The split chiral phonons further shift separately in the presence of an external magnetic field. Our results highlight magnetic dopants as an important approach of tuning chiral phonons in TMDCs.