  We compute the Chow group of a Ch{\^a}telet surface over a dyadic field.
Combined with the previous work of Bloch, Colliot-Th{\'e}l{\`e}ne, Coray,
Ischebeck, Sansuc, Swinnerton-Dyer, and the author, this allows one to compute
the Chow group of any Ch{\^a}telet surface over any number field.
