  Context. The existence of lithium-rich low-mass red giant stars still
represents a challenge for stellar evolution models. Stellar clusters are
privileged environments for this kind of investigation. Aims. To investigate
the chemical abundance pattern of the old open cluster Trumpler\,5, we observed
a sample of four red-clump stars with high-resolution optical spectrographs.
One of them (#3416) reveals extremely strong lithium lines in its spectrum.
Methods. One-dimensional, local thermodynamic equilibrium analysis was
performed on the spectra of the observed stars. A 3D-NLTE analysis was
performed to derive the lithium abundance of star #3416. Results. Star #3416 is
super Li-rich with A(Li)=3.75\,dex. The lack of $^6$Li enrichment
($^6$Li/$^7$Li$<$2%), the low carbon isotopic ratio
($^{12}$C/$^{13}$C=14$\pm$3), and the lack of evidence for radial velocity
variation or enhanced rotational velocity ($v\sin i = 2.8\,$\kms) all suggest
that lithium production has occurred in this star through the Cameron & Fowler
mechanism. Conclusions. We identified a super Li-rich core helium-burning,
red-clump star in an open cluster. Internal production is the most likely cause
of the observed enrichment. Given the expected short duration of a star's
Li-rich phase, enrichment is likely to have occurred at the red clump or in the
immediately preceding phases, namely during the He-flash at the tip of the red
giant branch (RGB) or while ascending the brightest portion of the RGB.
