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The discovery of lithium-rich giants contradicts expectations from canonical stellar evolution. Here we report on the serendipitous discovery of 20 Li-rich giants observed during the Gaia-ESO Survey, which includes the first nine Li-rich giant stars known towards the CoRoT fields. Most of our Li-rich giants have near-solar metallicities, and stellar parameters consistent with being before the luminosity bump. This is difficult to reconcile with deep mixing models proposed to explain lithium enrichment, because these models can only operate at later evolutionary stages: at or past the luminosity bump. In an effort to shed light on the Li-rich phenomenon, we highlight recent evidence of the tidal destruction of close-in hot Jupiters at the sub-giant phase. We note that when coupled with models of planet accretion, the observed destruction of hot Jupiters actually predicts the existence of Li-rich giant stars, and suggests Li-rich stars should be found early on the giant branch and occur more frequently with increasing metallicity. A comprehensive review of all known Li-rich giant stars reveals that this scenario is consistent with the data. However more evolved or metal-poor stars are less likely to host close-in giant planets, implying that their Li-rich origin requires an alternative explanation, likely related to mixing scenarios rather than external phenomena., This work is based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 188.B-3002. These data products have been processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge, and by the FLAMES/UVES reduction team at INAF/Osservatorio Astrofisico di Arcetri. These data have been obtained from the $\textit{Gaia}$-ESO Survey Data Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the UK Science and Technology Facilities Council. This work was partly supported by the European Union FP7 programme through ERC grant number 320360 and by the Leverhulme Trust through grant RPG-2012-541. We acknowledge the support from INAF and the Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR) in the form of the grant Premiale VLT 2012 and the Chemical and Dynamical Evolution of the Milky Way and Local Group Galaxies (prot. 2010LY5N2T). The results presented here benefit from discussions held during the $\textit{Gaia}$-ESO workshops and conferences supported by the ESF (European Science Foundation) through the GREAT Research Network Programme. GR acknowledges support from the project grant ‘The New Milky Way’ from the Knut and Alice Wallenberg Foundation. GMK is supported by the Royal Society as a Royal Society University Research Fellow. LS acknowledges support provided by the Chilean Ministry of Economy, Development, and Tourism's Millennium Science Initiative through grant IC120009, awarded to the Millennium Institute of Astrophysics, MAS. Funding for the Stellar Astrophysics Centre is provided by the Danish National Research Foundation. The research is supported by the ASTERISK project (ASTERoseismic Investigations with SONG and Kepler) funded by the European Research Council (Grant agreement no. 267864). VSA acknowledges support from VILLUM FONDEN (research grant 10118). SLM acknowledges support from the Australian Research Council through DECRA fellowship DE140100598. TM acknowledges financial support from Belspo for contract PRODEX Gaia-DPAC. JM acknowledges the support from the European Research Council Consolidator Grant funding scheme (project STARKEY, G.A. no. 615604). This research has made use of the ExoDat Database, operated at LAM-OAMP, Marseille, France, on behalf of the CoRoT/Exoplanet programme. This research made use of astropy, a community-developed core python package for Astronomy (Astropy Collaboration et al. 2013). This research has made use of NASA's Astrophysics Data System Bibliographic Services., This is the final version of the article. It first appeared from Oxford University Press via http://dx.doi.org/10.1093/mnras/stw1512