The existence of a charge density wave (CDW) in transition metal dichalcogenide CuS2 has remained undetermined since its first experimental synthesis nearly 50 years ago. Despite conflicting experimental literature regarding its low temperature structure, there exists no theoretical study of the phonon properties and lattice stability of this material. By studying the first-principles electronic structure and phonon properties of CuS2 at various electronic temperatures, we identify temperature-sensitive soft phonon modes which unveil a previously unreported Kohn anomaly at approximately 100K. Variation of the electronic temperature shows the presence of two distinct phases, characterized at low temperature by a 2×2×2 periodic charge modulation associated with the motion of the S2 dimers. Investigation of the Fermi surface presents a potential Fermi surface nesting vector related to the location of the Kohn anomaly and observed band splittings in the unfolded bandstructure. The combination of these results suggests a strong possibility of CDW order in CuS2. Further study of CuS2 in monolayer form finds no evidence of a CDW phase, as the identified bulk periodic distortions cannot be realized in 2D. This behavior sets this material apart from other transition metal dichalcogenide materials, which exhibit a charge density wave phase down to the 2D limit. As CDW in TMDC materials is considered to compete with superconductivity, the lack of CDW in monolayer CuS2 suggests the possibility of enhanced superconductivity relative to other transition metal dichalcogenides. Overall, our work identifies CuS2 as a previously unrealized candidate to study interplay of superconductivity, CDW order, and dimensionality.