This past Sunday, independent security contractors employed by Blackwater, a North Carolina based State Department private security contractor, were accused by the Iraqi government of opening fire--unprovoked--on a group of civilians, killing eight of them, and wounding thirteen. At the time the security personnel opened fire, they were escorting US State Department officials. There was, reportedly, an explosion near the convoy, and an unnamed embassy official is reported as saying that the contractors merely "escalated force to defend themselves." The Iraqi government, however, maintained that "the security company contractors opened fire randomly on the civilians," announcing, "[w]e consider this act a crime."
The Iraqi government has since revoked Blackwater's license to operate in Iraq, forcing the withdrawal of Blackwater's remaining 1,000-1,500 employees stationed there. However, a spokesperson for the Iraqi Ministry of the Interior--Brig. Gen. Abdul Karim Khalaf--announced Iraqi government's further intent to prosecute the specific Blackwater employees involved in the incident. According to the NY Times, "[t]he deaths struck a nerve with Iraqis, who say that private security firms are often quick to shoot and are rarely held responsible for their actions."
While Iraq is asserting the jurisdiction to try the Blackwater employees (after a "fair probe" in conjunction with US officials), it is not clear from whence it is asserting that power. According to Professor Scott Silliman, a former Air Force Judge Advocate General who now heads Duke Law School's Center of Law, Ethics and National Security, there is doubt over whether Iraq can 'lawfully' try the contractors. As he explains
Before the sovereign state of Iraq came into being, of course, we had the Coalition Provisional Authority (CPA) that was in charge of affairs in Baghdad. And, an order passed by the CPA in early 2004 exempted civilian contractors in Iraq from the jurisdiction of the Iraqi courts. I think the United States will argue  that still applies, although the Iraqis might try to come back and say, 'Well, we're a sovereign nation now; we have jurisdiction.'
As Silliman also explains, US Federal Courts do have jurisdiction over the private security contractors--stemming from the Military Extraterritorial Jurisdiction Act (2000)--as long as their employment supports the mission of the DOD overseas. Earlier this year, Congress also passed a law authorizing the treatment of civilian military contractors under the Uniform Code of Military Justice, although guidelines for treatment of civilian personnel under the Code have yet to be issued.
When it comes to resolving which government will actually handle any resulting trial, Silliman believes
It's going to be a diplomatic matter. The Secretary of State, obviously, is going to tell the Iraqis that we will investigate; that if a crime has been committed, we have the vehicle to bring them to prosecution. I just do not see the United States government allowing US nationals working for the US government to go before the Iraqi courts. Because, once you start down that path, then the next thing is, they'll want jurisidiction over our military personnel as well, and that's just not about to happen.
You can listen to the entire interview with Professor Silliman here.