  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 (62.9\pm 1.9\pm 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 (3899.0\pm 3.6\pm 4.9) MeV/c^2 and a width of (46\pm 10\pm
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)}=(21.5\pm 3.3\pm
7.5)%. In all measurements the first errors are statistical and the second are
systematic.
