We study the process e+e- to pi+pi-J/psi at a center-of-mass energy of 4.260 GeV using a 525 pb^{-1} data sample collected with the BESIII detector operating at the Beijing Electron Positron Collider. The Born cross section is measured to be (62.9pm 1.9pm 3.7) pb, consistent with the production of the Y(4260). We observe a structure at around 3.9 GeV/c^2 in the pi^pm J/psi mass spectrum, which we refer to as the Z_c(3900). If interpreted as a new particle, it is unusual in that it carries an electric charge and couples to charmonium. A fit to the pi^pm J/psi invariant mass spectrum, neglecting interference, results in a mass of (3899.0pm 3.6pm 4.9) MeV/c^2 and a width of (46pm 10pm 20) MeV. Its production ratio is measured to be R=frac{sigma(e+e- to pi^pm Z_c(3900)^mp to pi+pi-J/psi))} {sigma(e+e- to pi+pi-J/psi)}=(21.5pm 3.3pm 7.5)%. In all measurements the first errors are statistical and the second are systematic.
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