We present early high-resolution spectroscopic observations of the nova V1369 Cen. We have detected an absorption feature at 6695.6 Å that we have identified as blueshifted 7Li i λ6708 Å. The absorption line, moving at -550 km s-1, was observed in five high-resolution spectra of the nova obtained at different epochs. Based on the intensity of this absorption line, we infer that a single nova outburst can inject in the Galaxy {M}{Li} = 0.3-4.8 × 10-10 {M}⊙ . Given the current estimates of the Galactic nova rate, this amount is sufficient to explain the puzzling origin of the overabundance of lithium observed in young star populations.