So far, the hospital has said a team led by reconstructive surgeon Dr. Maria Siemionow used a donation from a woman who died to replace 80 percent of another woman's disfigured face.
The patient's name and age have not been released, and the Clinic says her family wants the reason for her surgery to remain confidential.
The transplant was the fourth worldwide. Two have been done in France, and one was performed in China.
The first of these transplants took place in France three years ago on a woman who had been mauled by her dog. CBS News correspondent Sheila MacVicar reports on that woman's recovery and how she is dealing with a new face.
Three years later, the French woman who underwent the world's first face transplant says she is still struggling to come to terms with what she sees in the mirror every day.
Isabelle Dinoire said in an interview last month that "it takes an awful lot of time to get used to someone else's face. It's a peculiar type of transplant."
Dinoire was given a new nose, mouth, and chin during surgery in France in 2005, and the operation worked. In spite of some signs of immune rejection, she soon regained sensation back in her face, and the operation continues to be a success.
What does she see? Not her old face, but something that is halfway between what she looked like and what the deceased donor looked like.
"The patient in France, when I had the opportunity to talk to her, she really was very excited about her new face and absolutely had no regrets and as a matter of fact, she said she would go for it anytime in the future," said Dr. Bohdan Pomahac, a plastic surgeon.
It turns out that face transplants are more complicated psychologically for patients -- and even for doctors -- than any other transplant, and thus more controversial.
The bold operation in the U.S. was carried out by reconstructive surgeon Marie Siemionow, a leader in the field.
And as more of these operations happen, they give hope to people who would otherwise not live normal lives. As the first face transplant patient says of her new face "It's part of me. I have the feeling of looking at something beautiful."
Dr. Mark Smith, a reconstructive plastic surgeon at Beth Israel Medical Center in New York, visited The Early Show to shed more light on the procedure. To see his interview with co-anchor Julie Chen, which follows the update on Isabelle Dinoire, click the Play button below.