The hierarchy may vary slightly depending on the type of hospital, but it is generally as follows:
At the top you have the Board of Directors, of which the President and CEO and the Chief of Medical Staff are Members. Below the President and CEO, you have various Vice Presidents (like of HR, Planning, and Corporate Affairs).
Below the Chief of Medical Staff, you have the various Chiefs of the Medical Specialities (e.g., OB/GYN, Emergency Medicine, Medicine, Anesthesiology, etc.). Below the Vice Presidents, there are the staff members of the various parts of the hospital, such as IS, Finance, HIM, Purchasing, etc.
So in a teaching hospital, residents would be covered under the chiefs of the medical specialties; the longer you've been a resident, the higher in the hierarchy you'd become.
a health info management text from AHIMA