  We bring the theoretical issue of whether two important cosmological demands,
baryon asymmetry and degenerate neutrinos as hot dark matter, can be compatible
in the context of the seesaw mechanism. To realize leptogenesis with almost
degenerate Majorana neutrinos without severe fine-tuning of parameters, we
propose the hybrid seesaw mechanism with a heavy Higgs triplet and right-handed
neutrinos. Constructing a minimal hybrid seesaw model with SO(3) flavor
symmetry for the neutrino sector, we show that the mass splittings for the
atmospheric and solar neutrino oscillations which are consistent with the
requirements for leptogenesis can naturally arise.
