Arizona has a mandatory "E-verify" law. Arizona's law suspends or revokes businesses' licenses if they employ illegal aliens unauthorized to work in the U.S. It also mandates the use of "E-Verify," a federal program permitting electronic verification of an employee's authorization to work in the US.
The Chamber of Commerce and civil rights groups argued that the Arizona law is preempted by federal immigration law. All lower courts disagreed, and so did the Supreme Court.
In a fractured opinion, the Court held that the federal Immigration Reform and Control Act does not stop Arizona from either suspending business licenses or requiring use of E-Verify. In fact, the law only requires employers to use E-Verify if they wish to rely on a "good faith" defense to proof that the employer is employing unauthorized workers.
Justice Kagan did not participate, and only four justices concurred in parts of the opinion. However, the continued viability of the Arizona law was upheld 5-3. So, Arizona is free to require employers to employ only authorized workers or risk losing the right to operate in Arizona.
The case is Chamber of Commerce v. Whiting and the opinion is here.