  We perform a systematic study of the odd-even mass staggering generated using
a pairing interaction computed at first order in low-momentum interactions.
Building on previous work including the (nuclear plus Coulomb) two-nucleon
interaction only, we focus here on the first-order contribution from chiral
three-nucleon forces. We observe a significant repulsive effect from the
three-nucleon interaction. The combined contribution from two- and
three-nucleon interactions accounts for approximately 70% of the experimental
pairing gaps. This leaves room for higher-order contributions to the pairing
kernel and the normal self-energy that need to be computed consistently.
