This is old news, but may not be widely known, and touches upon several discussion threads over the years.

Listed on the US Congress' website, in an appendix of laws found to be unconstitutional:

Supreme Court October Term
2006

Case
Parents Involved in Community Schools v. Seattle School District No. 1,
551 U.S. 701 (2007)

Author(s) of Opinion
Roberts, John

Subject Matter(s)
Civil Rights Law

Federal or State Position(s)
State and Local

Description of Unconstitutional Provision(s)
Policy of Seattle public schools using students' race as one of a series of "tiebreakers" to determine which high school students would attend.
Policy of Jefferson County public schools, in Kentucky, assigning some students to different schools if student's race would contribute to racial imbalance.

Constitutional Provision(s) Invoked
U.S. Const. amend. XIV

Constitutional Clause(s) Invoked
Equal Protection Clause