We consider a spinless fermionic p +/- ip superfluid living on a two-dimensional sphere. Using superfluid hydrodynamics, we show that the ground state necessarily exhibits topological defects: either a pair of elementary vortices or a domain wall between p +/- ip phases. In the topologically nontrivial BCS phase we identify the chiral fermion modes localized on the topological defects and compute their low-energy spectrum.