  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.
