[en] This study presents a theoretical approach to investigate the distinguishing features of surface plasmon polaritons (SPPs) at the interface of graphene and a four-level chiral atomic medium. The SPPs show the left and the right circularly polarized (LCP and RCP) propagation modes due to the cross coupling of electric and magnetic fields in the chiral medium. The two propagation modes of the SPPs are controlled with the strengths of control fields and their corresponding phases under the effect of Kerr nonlinearity (KNL). A 0.15 radian angle of divergence is calculated between the LCP and RCP modes of the SPPs under the effect of KNL, which is further modified to 0.5 radian with the strengths of control fields at a propagation length equal to $80{\mathrm{\lambda <!--\; ??\; -->}}_0$. The possibility of such hybrid mode SPPs propagation may result into new technological applications in the design of more compact nano-photonic devices.