Broken symmetry within a superconductor can give rise to unconventional properties, such as mixed-parity Cooper pairing in non-centrosymmetric materials. Despite the expectation that such broken symmetry should show up in the electronic state, its spectroscopic detection has proven to be a challenge due to the absence of a suitable measurement platform. In this study, we have discovered a naturally occurring chirality in a superconducting monolayer of NbSe₂ grown on graphene using molecular beam epitaxy. This chirality disrupts both inversion and reflection symmetries, making this atomically thin, twisted superconductor an ideal candidate for examining the influence of chirality on superconductivity via spectroscopic-imaging scanning tunneling microscopy. Our successful imaging of interference patterns exhibited by Bogoliubov quasiparticles with wave vectors that do not align with any combinations of NbSe₂ and graphene primary lattice vectors suggests that superconductivity within this chiral structure can manifest in a manner that does not align with the atomic potential landscape.