The production of the hypertriton nuclei ainer hidden"> and ainer hidden"> has been measured for the first time in Pb–Pb collisions at ainer hidden"> with the ALICE experiment at LHC. The pTainer hidden">-integrated ainer hidden"> yield in one unity of rapidity, ainer hidden"> 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 B3ainer hidden"> shows a dependence on the transverse momentum, similar to the B2ainer hidden"> of deuterons and the B3ainer hidden"> of 3He nuclei. The ratio of yields ainer hidden"> was measured to be S3=0.60±0.13(stat.)±0.21(syst.)ainer hidden"> in 0–10% centrality events; this value is compared to different theoretical models. The measured S3ainer hidden"> is compatible with thermal model predictions. The measured ainer hidden"> lifetime, ainer hidden"> is in agreement within 1σ with the world average value.