We present the discovery of a 70 kpc X-ray tail behind the small late-type galaxy ESO 137-001, in the nearby, hot (T = 6.5 keV) merging cluster A3627, from both Chandra and XMM-Newton observations. The tail has a length-to-width ratio of ∼10. It is luminous (L0.5–2 keV ∼ 1041 ergs s-1), with a temperature of ∼0.7 keV and an X-ray Mgas of ∼109 M⊙ (∼10% of the galaxy's stellar mass). We interpret this tail as the stripped interstellar medium of ESO 137-001 mixed with the hot cluster medium, with this blue galaxy being converted into a gas-poor galaxy. Three X-ray point sources are detected in the axis of the tail, which may imply active star formation there. The straightness and narrowness of the tail also imply that the turbulence in the intracluster medium is not strong on scales of 20–70 kpc.