Is the CISG is a self-executing treaty?

On today's ContractsProf Blog, there are interesting comments on whether CISG is a self-executing treaty under the Supreme Court's recent ruling in Medellin v. Texas, with Prof. Michael Van Alstine of Maryland opining that it is and Prof. Michael Zimmer of Seton Hall unpersuaded that a court would necessarily so find. The concern of contracts and commercial law scholars is that if CISG is not held to be a self-executing treaty, state courts may be free to refuse to follow CISG in international sales disputes litigated in state courts.