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The paper analyzes a three-layer waveguide made of chiral metamaterials separated by the graphene interface. The interface consists of three graphene monolayers with a thickness 0.34 nm, so the interface thickness is 1.02 nm. Mathematical formulas are derived for dispersion relations and power flux of guided waves for hybrid odd and even modes at right and left circular polarizations. Power profiles in the waveguide regions are potted and discussed. The work aims to investigate changes that occur due to the graphene presence as an interface in the chiral slab waveguide. It is shown that graphene properties affect the light propagation, which, in turn, provides a disappearance of the fundamental odd mode. The power flux through the waveguide shows a significant effect due to the presence of graphene and chirality. [ABSTRACT FROM AUTHOR]