  ${}^{3}P_{2}$ superfluids realized in neutron stars are the largest
topological quantum matters in our Universe. We establish the existence and
stability of non-Abelian half-quantum vortices (HQVs) in ${}^{3}P_{2}$
superfluids with strong magnetic fields. Using a self-consistent microscopic
approach, we find that a singly quantized vortex is energetically destabilized
into a pair of two non-Abelian HQVs owing to the strongly spin-orbit-coupled
pairing. We find a topologically protected Majorana fermion on each HQV,
thereby providing two-fold non-Abelian anyons characterized by both Majorana
fermions and a non-Abelian first homotopy group.
