  Linear, suspended chains of magnetic atoms proximity coupled to an s-wave
superconductor are predicted to host Majorana zero modes at the chain ends in
the presence of strong spin-orbit coupling. Specifically, iron (Fe) chains on
Pb(110) have been explored as a possible system to exhibit topological
superconductivity and host Majorana zero-modes [Nadj-Perge, et al., Science
346, 602 (2014)]. Here, we study chains of the transition metal cobalt (Co) on
Pb(110) and check for topological signatures. Using spin-polarized scanning
tunneling spectroscopy, we resolve ferromagnetic order in the $d$ bands of the
chains. Interestingly, also the subgap Yu-Shiba-Rusinov (YSR) bands carry a
spin polarization as was predicted decades ago. Superconducting tips allow us
to resolve further details of the YSR bands and in particular resonances at
zero energy. We map the spatial distribution of the zero-energy signal and find
it delocalized along the chain. Hence, despite of the ferromagnetic coupling
within the chains and the strong-spin orbit coupling in the superconductor, we
do not find clear evidence of Majorana modes. Simple tight-binding calculations
suggest that the spin-orbit-split bands may cross the Fermi level four times
which suppresses the zero-energy modes.
