Hinchingbrooke Hospital, in Cambridgeshire, has now returned to NHS management after Circle pulled out of its 10-year contract in January.
The hospital was placed in special measures after a Care Quality Commission (CQC) report.
Chairman Alan Burns said he would be looking at the "viability of services".
But he said his immediate priorities were to oversee "a smooth transition" from Circle back to NHS management and to get the hospital out of special measures.
Mr Burns, a retired NHS chief executive, was appointed to chair the new NHS board running Hinchingbrooke, by the NHS Trust Development Authority.
He said there was a "a very good sustainable future" for the hospital.
But he added: "It's not rocket science to know there are some things the population of Huntingdonshire only just makes viable.
"Doctors and nurses need a volume of cases to retain the quality of the work they do - there are only so many accident and emergency, orthopaedic and maternity cases in Huntingdonshire in any one year.
"So when that number is close to the guidelines for the viability of services, it's right that you look at it."
Circle took on Hinchingbrooke in early 2012, as it was facing closure.
Three years into its contract, the company announced the franchise was "no longer viable under current terms".
At the same time, the CQC rated Hinchingbrooke "inadequate", highlighting particular concerns over accident and emergency and medical care, although Circle disputed its findings.
The new chairman of the first hospital in the NHS to be run by a private company has said he cannot rule out department closures.