Doctors and staff members posted pictures and videos of this process from start to finish.
In the first series of pictures posted, the donor heart arrived at an airport in Dallas.
The patient is a woman in her later 30's who is married with a teenaged daughter.
She was born with an abnormal left ventricle and developed bacterial infection at three months old.
Videos posted on the hospitals Twitter feed show the doctors removing the patient's damaged heart.
This is the 200th heart transplant for this team.
Pictures showed the doctors making the first connections and the first time the patient's blood flowing through the new heart.
Then, the echocardiogram showed the patient's new heart beating on its own.
The patient will spend the next few days in ICU and will start cardiac rehab.
All the details can be found by using #HeartTXLive.