BATON ROUGE, La. — A large blue sign stood at the entrance to the Delta Clinic, a low brick building amid the ranch houses in a neighborhood here in the Louisiana capital.

“This Clinic Stays Open” it read in white letters, and indeed, on Thursday afternoon there were the usual security officer, the men with fliers and large wooden crucifixes waiting out on the sidewalk and the steady stream of young women pulling in and out of the parking lot, seeking to end their pregnancies. What was missing, after 36 years, was anyone who could perform an abortion.

On Wednesday, a three-judge panel of the Court of Appeals for the Fifth Circuit unanimously voted to allow a 2014 state law requiring abortion doctors to have admitting privileges at nearby hospitals to go immediately into effect. After the law passed, five of the six abortion doctors in the state — including the doctor who performs abortions at Delta Clinic — applied and were turned down at the hospitals near to at least one of the clinics where they work (several of the doctors work at multiple clinics).

The appeals court decision, which is expected to be the subject of an emergency appeal to the Supreme Court, means that one of the state’s four remaining clinics closed completely on Thursday and another, Delta, could provide consultations only. A third, in Shreveport, is operating but may not be able to hang on for very long. If it closed, it would leave one abortion doctor in New Orleans, in a state where 10,000 abortions are performed a year.