Lithium rich stars in globular clusters are rare .
In fact , only 14 have been found so far , in different evolutionary phases from dwarfs to giants .
Different mechanisms have been proposed to explain this enhancement , but it is still an open problem .
Using spectra collected within the Gaia-ESO Survey , obtained with the GIRAFFE spectrograph at the ESO Very Large Telescope , we present the discovery of the first Li-rich star in the cluster NGC 1261 , the second star known in the red giant branch bump phase .
The star shows an extreme Li overabundance of A ( Li ) _ { LTE } = 3.92 \pm 0.14 , corresponding to A ( Li ) _ { NLTE } = 3.40 dex .
We propose that the Li enhancement is caused by fresh Li production through an extra mixing process ( sometimes referred to as cool bottom burning ) or could be a pre-existing Li overabundance resulting from binary mass transfer , likely from a red giant branch star , because of the low barium abundance .
To unambiguously explain the Li enhancement in globular cluster stars , however , a reliable determination of the abundance of key species like Be , ^ { 6 } Li , ^ { 12 } C/ ^ { 13 } C , and several s-process elements is required , as well as detailed modeling of chromospheric activity indicators .