The lone opinion from the US Supreme Court today is a civil case, Virginia Office for Protection and Advocacy v. Stewart, No. 09-529.

We consider whether Ex parte Young, 209 U. S. 123 (1908), allows a federal court to hear a lawsuit for prospective relief against state officials brought by another agency of the same State.

Answer: yes (6-2, Kagan recused).

VOPA is an office set up to advocate for the disabled, but this could easily happen with a criminal defense agency with an overly broad view of its mission.  So Young and the Eleventh Amendment aren't going to kill such a suit.

Justice Kennedy, concurring joined by Justice Thomas, tells us that state law, not federal law, is the way to stop the absurdity of the state suing itself:

First, and most important, state law must authorize an agency or official to sue another arm of the State. If States do not wish to see their internal conflicts aired in federal court, they need not empower their officers or agencies to sue one another in a federal forum. And if state officers are not by state law empowered to sue, they may invoke federal jurisdiction only in their personal capacities. 

Second, to the extent there is some doubt under state law as to an officer's or agency's power to sue, or any other state-law issue that may be dispositive, federal courts should abstain under Railroad Comm'n of Tex. v. Pullman Co., 312 U. S. 496 (1941).

This opinion should have a bit more clout than most concurrences, as Justices Kennedy and Thomas are necessary votes for the majority.  Had they joined the dissent, it would have been a 4-4 affirmance by an equally divided court.