The solar neutrino problem, atmospheric neutrino problem and the hot dark matter which seems to be required by galaxy formation can all be most economically described by three very degenerate neutrinos with a common mass of a few eV. Such neutrino masses could also be relevant for the recent data on double beta decay. We provide an existence proof for such a scenario by constructing an explicit model in which the desired hierarchy of neutrino mass splittings arises naturally.