The production of the hypertriton nuclei den">de"> and den">de"> has been measured for the first time in Pb–Pb collisions at de095d1ff824360d8f4b21694d">den">de"> with the ALICE experiment at LHC. The pTden">de">-integrated den">de"> yield in one unity of rapidity, den">de"> in the 0–10% most central collisions, is consistent with the predictions from a statistical thermal model using the same temperature as for the light hadrons. The coalescence parameter de7fe0908d1e417a399d" title="Click to view the MathML source">B3den">de"> shows a dependence on the transverse momentum, similar to the B2den">de"> of deuterons and the de7fe0908d1e417a399d" title="Click to view the MathML source">B3den">de"> of 3He nuclei. The ratio of yields den">de"> was measured to be S3=0.60±0.13(stat.)±0.21(syst.)den">de"> in 0–10% centrality events; this value is compared to different theoretical models. The measured S3den">de"> is compatible with thermal model predictions. The measured den">de"> lifetime, den">de"> is in agreement within 1σ with the world average value.