Spin-triplet superconductivity is a condensate of electron pairs with spin-1 and an odd-parity wavefunction. A particularly interesting manifestation of triplet pairing is a chiral p-wave state which is topologically non-trivial and a natural platform for realizing Majorana edge modes. Triplet pairing is however rare in solid state systems and so far, no unambiguous identification has been made in any bulk compound. Since pairing is most naturally mediated by ferromagnetic spin fluctuations, uranium based heavy fermion systems containing f electron elements that can harbor both strong correlations and magnetism are considered ideal candidate spin-triplet superconductors. In this work we present scanning tunneling microscopy (STM) studies of the newly discovered heavy fermion superconductor, UTe2 with a T$_{SC}$ of 1.6 K. We find signatures of coexisting Kondo effect and superconductivity which show competing spatial modulations within one unit-cell. STM spectroscopy at step edges show signatures of chiral in-gap states, predicted to exist at the boundaries of a topological superconductor. Combined with existing data indicating triplet pairing, the presence of chiral edge states suggests that UTe2 is a strong candidate material for chiral-triplet topological superconductivity.