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In this letter we characterise IRAS12556-7731 as the first lithium-richM-type giant. Based on its late spectral type and high lithium content, andbecause of its proximity in angular distance to the ChamaeleonII star-formingregion, the star was misclassified as a young low-mass star in a previous work.Based on HARPS data, synthetic spectral modelling, and proper motions, wederive the astrophysical parameters and kinematics of the star and discuss itsevolutionary status. This solar-mass red giant (Teff=3460+/-60K andlog(g)=0.6+/-0.2) is characterised by a relatively fast rotation (vsin(i)~8km/s), slightly subsolar metallicity and a high-lithium abundance,A(Li)=2.4+/-0.2dex. We discuss IRAS12556-7731 within the context of other knownlithium-rich K-type giants. Because it is close to the tip of the red giantbranch, IRAS12556-7731 is the coolest lithium-rich giant known so far, and itis among the least massive and most luminous giants where enhancement oflithium has been detected. Among several possible explanations, we cannotpreclude the possibility that the lithium enhancement and rapid rotation of thestar were triggered by the engulfment of a brown dwarf or a planet.

IRAS12556-7731: a "chamaeleonic" lithium-rich M-giant