The link between chirality in the fermion sector and (anti-)self-duali
ty in the boson sector is reexamined in the light of Connes' noncommut
ative geometry approach to the Standard Model. We find it to impose th
at the noncommutative Yang-Mills action be symmetrized in an analogous
way to the Dirac-Yukawa operator itself. (C) 1998 Elsevier Science B.
V.