  We use a recently improved version of the chiral nucleon-nucleon potential at
next-to-next-to-leading order to calculate the $^1S_0$ pairing gap in
isospin-symmetric nuclear matter. The pairing potential consists of the
long-range one- and two-pion exchange terms and two short-distance NN-contact
couplings. We find that the inclusion of the two-pion exchange at
next-to-next-to-leading order reduces substantially the cut-off dependence of
the $^1S_0$ pairing gap determined by solving a regularised BCS equation. Our
results are close to those obtained with the universal low-momentum
nucleon-nucleon potential $V_{\rm low-k}$ or the phenomenological Gogny D1S
force.
