A Neurosurgeon is a surgeon who specializes in the treatment of disorders of the brain, spine, peripheral nerves, and the blood vessels surrounding these areas.
In addition to basic medical training, neurosurgeons serve a residency of five to seven years, and then either take a senior residency or fellowship in a sub-speciality, such as pediatric neurosurgery.
Neurosurgery is the most competive and well paid medical specialty. Less than 1% of all physicians in the United States practice in the field and the chance of even a well qualified intern getting chosen for a residency is less than 60%.
Chase was chosen for a neurosurgery residency, but only completed one year of the program.
The lack of a neurosurgeon at the hospital led to the events in the episode Now What? when the team, while House was busy, had to treat Dr. Richardson.