Board Thread:Off-Topic/@comment-15575766-20140728041820/@comment-3153244-20140728054711

Bureaucrats can only add the groups Bureaucrat, Rollback and Administrator, and can remove the rights Rollback, Administrator and Bot. It's only if you also have the Administrator right that you can add/remove Chat Mod rights, although bureaucrat users should already have that admin group added to their user to do tasks such as blocking and deleting pages. More info at Special:ListGroupRights.