Constraints on $|U_{e3}|^2$ from a Three-Neutrino Oscillation Analysis of the CHOOZ Data

Results of a new analysis of the CHOOZ data, performed in the framework of three-neutrino mixing, are presented. Both the cases of normal and inverted neutrino mass hierarchy are considered. The parameters characterizing the solar neutrino oscillations, $\Delta m^2_{\odot}$ and $\theta_{\odot}$, are assumed to lie in the region of the large mixing angle (LMA) MSW solution of the solar neutrino problem. For $\Delta m^2_{\odot}$ not exceeding $10^{-4} eV^2$ the new CHOOZ exclusion curve in the $\Delta m^2_{31} - |U_{e3}|^2$ plane practically coincides with the exclusion curve obtained in the two-neutrino mixing case. For $\Delta m^2_{\odot}$ bigger than or equal to $2x10^{-4} eV^2$, the constraints of the CHOOZ data on $|U_{e3}|^2$ are more stringent than those obtained in the two- neutrino oscillation analysis.