Galaxy clusters grow primarily through the continuous accretion of group-scale haloes. Group galaxies experience preprocessing during their journey into clusters. A star-bursting compact group, the Blue Infalling Group (BIG), is plunging into the nearby cluster A1367. Previous optical observations reveal rich tidal features in the BIG members, and a long H$alpha$ trail behind. Here we report the discovery of a projected $sim 250$ kpc X-ray tail behind the BIG using Chandra and XMM-Newton observations. The total hot gas mass in the tail is $sim 7times 10^{10} {rm M}_odot$ with an X-ray bolometric luminosity of $sim 3.8times 10^{41}$ erg s$^{-1}$. The temperature along the tail is $sim 1$ keV, but the apparent metallicity is very low, an indication of the multi-$T$ nature of the gas. The X-ray and H$alpha$ surface brightnesses in the front part of the BIG tail follow the tight correlation established from a sample of stripped tails in nearby clusters, which suggests the multiphase gas originates from the mixing of the stripped interstellar medium (ISM) with the hot intracluster medium (ICM). Because thermal conduction and hydrodynamic instabilities are significantly suppressed, the stripped ISM can be long lived and produce ICM clumps. The BIG provides us a rare laboratory to study galaxy transformation and preprocessing.