We report on the discovery and chemical abundance analysis of the first CEMP-r/s star detected in the Sagittarius dwarf spheroidal galaxy (Sgr dSph) by means of UVES high-resolution spectra. The star, found in the outskirts of Sgr dSph, along the major axis of the main body, is a moderately metal-poor giant (Teff=4753K, logg=1.75, [Fe/H]=-1.55) with [C/Fe]=1.13, placing it in the so-called "high-carbon band", and strong s-process and r-process enrichment ([Ba/Fe]=1.4, [Eu/Fe]=1.01). Abundances of 29 elements from C to Dy were obtained. The chemical pattern appears to be best fitted by a scenario where an r-process pollution event pre-enriched the material out of which the star was born as secondary in a binary system whose primary evolved through the AGB phase, providing C- and s-process enrichment.