Chiral phonons are vibrational modes in a crystal that possess a well-defined handedness or chirality, typically found in materials that lack inversion symmetry. Here, we report the discovery of chiral phonon modes in the kagome ferromagnetic Weyl semimetal Co_{3}Sn_{2}S_{2}, a material that preserves inversion symmetry but breaks time-reversal symmetry. Using helicity-resolved magneto-Raman spectroscopy, we observe the spontaneous splitting of the doubly degenerate in-plane E_{g} modes into two distinct chiral phonon modes of opposite helicity when the sample is zero-field cooled below the Curie temperature in the absence of an external magnetic field. As we sweep the out-of-plane magnetic field, this E_{g} phonon splitting exhibits a well-defined hysteresis loop directly correlated with the material's magnetization. The observed spontaneous splitting reaches up to 1.27 cm^{-1} at low temperatures, progressively diminishes with increasing temperature, and completely vanishes near the Curie temperature. Our findings highlight the role of the magnetic order in inducing chiral phonons, paving the way for novel methods to manipulate chiral phonons through magnetization and vice versa. Additionally, our Letter introduces new possibilities for controlling chiral Weyl fermions using chiral phonons.