The nature of the dominant pairing mechanism in some two-dimensional transition metal dichalcogenides is still debated. Focusing on monolayer 1H-NbSe2, we show that superconductivity can be induced by the Coulomb interaction when accounting for screening effects on the trigonal lattice with multiple orbitals. Using ab initio based tight-binding parametrizations for the relevant low-energy d-bands, we evaluate the screened interaction microscopically. In the direct space, we find pronounced Friedel oscillations, a key to the Kohn-Luttinger mechanism for superconductivity. The momentum-resolved gap equations predict at the critical temperature Tc two degenerate solutions of symmetry, signalling the unconventional nature of the pairing. Their complex linear combination, i.e., a chiral gap with p-like symmetry, provides the ground state of the model. Our prediction of a fully gapped chiral phase well below Tc is in good agreement with the spectral function extracted from tunnelling spectroscopy measurements.