  We study initial-state radiation events, $e^+e^- \to
\gamma_{ISR}\pi^+\pi^-J/\psi$, with data collected with the BaBar detector. We
observe an accumulation of events near 4.26 GeV/$c^2$ in the invariant-mass
spectrum of $\pi^+\pi^-J/\psi$. Fits of the mass spectrum indicate that a broad
resonance with a mass of about 4.26 GeV/$c^2$ is required to describe the
observed structure. The presence of additional narrow resonances cannot be
excluded. The fitted width of the broad resonance is 50 to 90 MeV/$c^2$,
depending on the fit hypothesis.
