A major challenge for future spintronics is to develop suitable spin transport channels with long spin lifetime and propagation length. Graphene can meet these requirements, even at room temperature. On the other side, taking advantage of the fast motion of chiral textures, that is, Neel-type domain walls and magnetic skyrmions, can satisfy the demands for high-density data storage, low power consumption, and high processing speed. We have engineered epitaxial structures where an epitaxial ferromagnetic Co layer is sandwiched between an epitaxial Pt(111) buffer grown in turn onto MgO(111) substrates and a graphene layer. We provide evidence of a graphene-induced enhancement of the perpendicular magnetic anisotropy up to 4 nm thick Co films and of the existence of chiral left-handed Neel-type domain walls stabilized by the effective Dzyaloshinskii-Moriya interaction (DMI) in the stack. The experiments show evidence of a sizable DMI at the gr/Co interface, which is described in terms of a conduction electron mediated Rashba-DMI mechanism and points opposite to the spin orbit coupling-induced DMI at the Co/Pt interface. In addition, the presence of graphene results in (i) a surfactant action for the Co growth, producing an intercalated, flat, highly perfect face-centered cubic film, pseudomorphic with Pt and (ii) an efficient protection from oxidation. The magnetic chiral texture is stable at room temperature and grown on insulating substrate. Our findings open new routes to control chiral spin structures using interfacial engineering in graphene-based systems for future spin-orbitronics devices fully integrated on oxide substrates.