We have serendipitously identified the first lithium-rich giant star located close to the red giant branch bump in a globular cluster. Through intermediate-resolution FLAMES spectra we derived a lithium abundance of A(Li)=2.55 (assuming local thermodynamical equilibrium), which is extremely high considering the stars evolutionary stage. Kinematic and photometric analysis confirm the object as a member of the globular cluster NGC 362. This is the fourth Li-rich giant discovered in a globular cluster but the only one known to exist at a luminosity close to the bump magnitude. The three previous detections are clearly more evolved, located close to, or beyond the tip of their red giant branch. Our observations are able to discard the accretion of planets/brown dwarfs, as well as an enhanced mass-loss mechanism as a formation channel for this rare object. Whilst the star sits just above the cluster bump luminosity, its temperature places it towards the blue side of the giant branch in the colour-magnitude diagram. We require further dedicated observations to unambiguously identify the star as a red giant: we are currently unable to confirm whether Li production has occurred at the bump of the luminosity function or if the star is on the pre zero-age horizontal branch. The latter scenario provides the opportunity for the star to have synthesised Li rapidly during the core helium flash or gradually during its red giant branch ascent via some extra mixing process.
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