For the first time since joining Quora, I found a question to which I can meaningfuly contribute. Thought you might like to see my answer.
Why would someone choose to be a chief resident (in internal medicine)?
The cynical answers would be "out of a misguided sense of loyalty to your program". The correct and not very useful answer is—it depends.
Most positions entail primarily administrative responsibilities, with some teaching and clinical duties, and a salary just slightly higher than that of a PGY-3. So, you can expect your patient care skills to languish unless you work on maintaining them, your teaching skills to be slightly improved—or at least no worse if you've had some prior experience—and your knowledge of hospital administration, people management, dealing with email, and making the most out of seemingly pointless meetings to go through the roof. If you have any interest in academic medicine, as a generalist and sub-specialist alike, this last skill set will be invaluable. It is also a stamp of approval of sorts for any fellowship program director looking at your CV if and when you apply.
You also have much more free time. Depending on how many chiefs your program has, it will be most or all weekends, and almost all federal holidays. This is a good time to study for the boards if you haven't taken them already, write up the research you've been working on, or spend some time with your family (the chief's maternity/paternity leave is usually more flexible, but that's program-dependent).
The downsides: you will have one fewer year of attending-level salary, so if you have a large debt or other financial responsibilities think twice before saying yes; some friendships you made with the junior residents will be undone or temporarily put on hold, unless you are very careful about not playing favorites; you may lose some respect for your higher-ups, as it goes whenever you peek behind the curtain; you will need to develop a thick skin, if you don't have one already. Some would say these last two are actually pluses. It depends.
Visa issues complicate the matter, but I won't go into details—bureaucracy shouldn't play a role in determining a career choice, and when there is will (your own as well as the program's) there is a way to bypass any obstacles.
Hope this helps.