  We investigate the current status of the long-wavelength vacuum oscillation
solution to the solar neutrino problem and to what extent the presence of a
third neutrino can affect and modify it. Assuming that the smaller mass squared
difference that can induce such oscillations, $\Delta m^2_{12}$, is in the
range $10^{-11}-10^{-8}$ eV$^2$ and the larger one, $\Delta m^2_{23}$, in the
range relevant to atmospheric neutrino observations, we analyze the most recent
solar neutrino data coming from Homestake, SAGE, GALLEX, GNO and
Super-Kamiokande experiments in the context of three neutrino generations. We
include in our vacuum oscillation analysis the MSW effect in the Sun, which is
relevant for some of the parameter space scrutinized. We have also performed,
as an extreme exercise, the fit without Homestake data. % While we found that
the MSW effect basically does not affect the best fitted parameters, it
significantly modifies the allowed parameter space for $\Delta m^2_{12}$ larger
than $\sim 3 \times 10^{-10}$ eV$^2$, in good agreement with the result
obtained by A. Friedland in the case of two generations. % Although the
presence of a third neutrino does not essentially improve the quality of the
fit, the solar neutrino data alone can give an upper bound on $\theta_{13}$,
which is constrained to be less than $\sim 60^\circ$ at 95 % C.L.
