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Graphene layers on semiconducting substrates, modified using covalent and noncovalent chemical functionalization, can be utilized for the fabrication of hybrid structures combining the physical properties of graphene and organic molecules. In this paper the results of investigations of the atomic and electronic structure of ultrathin graphene layers on β-SiC/Si(001) wafers modified using the phenazine dye Neutral Red are presented. Continuous graphene films consisting of several atomic layers are synthesized on β‑SiC/Si(001) wafers using high temperature annealing in ultrahigh vacuum. The synthesized graphene layers were chemically modified in a solution of diazonium salt of the Neutral Red dye under white-light illumination. The results of scanning tunneling microscopy and spectroscopy demonstrate the formation of a composite phenazine–graphene structure with a large energy gap in all surface regions. The molecules can be oriented preferentially parallel and perpendicular to the graphene layers and form locally ordered structures with rectangular and oblique unit cells. The electronic energy spectrum and band gap in different surface areas depend on the local atomic structure and the molecule’s orientation relative to the surface. According to density-functional-theory calculations, the local modifications of the electronic structure and band gap can be related to deformations (compression or extension) of the phenazine dye molecules because of their interaction with the uppermost graphene layer.