  Cyclic coverings produce many examples of topologically contractible smooth
affine complex varieties. In this paper, we study the motivic cohomology groups
of cyclic coverings over algebraically closed fields of characteristic $0$. In
particular, we prove that in many situations Chow groups of cyclic coverings
become trivial after tensoring with $\mathbb{Q}$. Furthermore, we can prove
that the Chow groups of certain bicyclic coverings are trivial even without
tensoring with $\mathbb{Q}$.
