My father was born with fairly severe Pectus Excavatum, or hollowed chest. In this birth defect, the growth of bone and cartilage in the chest wall is abnormal creating a sunken or hollow area that can push the heart and circulatory system out of position. This can result in health issues such as a rapid heartbeat and difficulty tolerating exercise. But he was still able to make it through jump school!
To learn more about this condition:
The Man With A Hollow Chest 