  The decay channel J/\psi --> \gamma \pi^+ \pi^- \eta^{\prime} is analyzed
using a sample of 5.8\times 10^7 J\psi events collected with the BESII
detector. A resonance, the X(1835), is observed in the \pi^+ \pi^-
\eta^{\prime} invariant mass spectrum with a statistical significance of 7.7
\sigma. A fit with a Breit-Wigner function yields a mass M = 1833.7 \pm
6.1(stat) \pm 2.7(syst) MeV/c^2, a width \Gamma = 67.7 \pm 20.3(stat) \pm
7.7(syst) MeV/c^2 and a product branching fraction B(J/\psi --> \gamma X) B(X
--> \pi^+ \pi^- \eta^{\prime}) = (2.2 \pm 0.4(stat) \pm 0.4(syst)) \times
10^{-4}. The mass and width of the X(1835) are not compatible with any known
meson resonance. Its properties are consistent with expectations for the state
that produces the strong p\bar{p} mass threshold enhancement observed in the
J\psi -->\gamma p \bar{p} process at BESII.
