As long as the foreign contractor is not a U.S. person and the services are wholly performed outside the U.S., then no Form 1099 is required and no withholding is required.
However (Treas. Reg. §1.1441-1(b)(3)), it is generally easier to ask them to complete a Form W-8BEN. By signing Form W-8BEN, the foreign contractor is certifying that he or she is not a U.S. person.
The Form W-8BEN is not filed with the I.R.S. It is kept on file with the U.S. payor in case the U.S. payor is audited. If audited, the Form W-8BEN supports why no Form 1099 was issued and why no tax was withheld.
