We study the process e+ e- →(D* D*)± π∓ at a center-of-mass energy of 4.26 GeV using a 827 pb(-1) data sample obtained with the BESIII detector at the Beijing Electron Positron Collider. Based on a partial reconstruction technique, the Born cross section is measured to be (137±9±15) pb. We observe a structure near the (D* D*)± threshold in the π∓ recoil mass spectrum, which we denote as the Zc±(4025). The measured mass and width of the structure are (4026.3±2.6±3.7) MeV/c2 and (24.8±5.6±7.7) MeV, respectively. Its production ratio σ(e+ e- → Zc±(4025)π∓ → (D* D*)± π∓)/σ(e+ e- → (D* D*)± π∓) is determined to be 0.65±0.09±0.06. The first uncertainties are statistical and the second are systematic.