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Recent experiments have shown that the charge density wave (CDW) lattice of 1T-TaS₂ can be observed within a graphene layer placed on top using scanning tunneling microscopy and spectroscopy (STM/STS)^1-3. This observation suggests the possibility of an unexplored proximity-induced CDW within graphene when placed in contact with 1T-TaS₂. The nature of such a novel CDW proximity effect is shown to involve short-range Coulomb and exchange interactions between itinerant Dirac electrons in graphene and localized electrons in 1T-TaS₂. We further explore the CDW proximity effect by probing the local electronic properties of graphene both on top of and in lateral contact with 1T-TaS₂ using STM and STS. Finally, we organize our results by relating the CDW proximity effect with well-known contact proximity effects such as the spin-orbit, magnetic, and superconducting proximity effects.