On the Status of Three-Neutrino Mixing

All existing solar and atmospheric neutrino oscillation data are described by the standard two-neutrino formulas with neutrino mass squared differences that satisfy the hierarchy relation $\mathrm{\Delta }{m}_{sol}^2\ll \mathrm{\Delta }{m}_{atm}^2$. We discuss this phenomenon from the point of view of three-neutrino mixing. Possibilities to see effects of three-neutrino mixing and, in particular, effects of CP-violation in the lepton sector depend on the values of $\mathrm{\mid }{U}_{e3}{\mathrm{\mid }}^2$ and $\mathrm{\Delta }{m}_{sol}^2$. We present an upper bound of $\mathrm{\mid }{U}_{e3}{\mathrm{\mid }}^2$, which was obtained from a three-neutrino analysis of CHOOZ data in the case if the solar neutrino oscillation parameters lie in the LMA allowed region.