Three flavor implications of CHOOZ result

We analyze the recent result of the CHOOZ collaboration in the context of mixing and oscillations between all the three neutrino flavors. If one assumes a hierarchy among the vacuum mass eigenvalues (\delta_{21} \ll \delta_{31}), then the CHOOZ result limits the (13) mixing angle \phi to quite small values. This in turn limits the contribution of the \nu_e <--> \nu_\mu oscillation channel to the atmospheric neutrino anomaly to less than 10 percent. It also implies that the solution to the solar neutrino problem is effectively \nu_e <--> \nu_\mu oscillation and that of the atmospheric neutrino problem is effectively \nu_\mu <--> \nu_\tau.