Recent neutron scattering experiments show that the spin-resonance modes appearing in the superconducting phase of Fe-based superconductors are more complex than a single singlet-triplet excitation. There is splitting in at least two modes, of which the one at lower energy is anisotropic in spin space and that at higher energy is isotropic. For an optimum electron-doped compound we could recently show that while the high-energy mode behaves in accordance to the singlet-triplet interpretation, the low energy mode exhibits an intrinsic chiral character. Here, we propose to analyse the possible chirality in a hole-doped compound, in which unpolarised neutron scattering finds an extraordinary strong low-energy mode, the strongest resonance reported for any Fe-based superconductor. Is the chiral character of this resonance mode even stronger than that detected for electron doping?