Should they?

Should the CIA have a chance to choose life or death for someone that doesn't live in America?

Elaborate please? Do you mean just any random person for no reason?

Hell no. What made you ask this? Any recent events?

Elaborate please? Do you just any random person for no reason?

Take Osama Bin Laden for instance, were we right in going after him? He was never a US resident.

Should the CIA have a chance to choose life or death for someone that doesn't live in America?

t;dr Nope.

Shouldn't be able to kill anyone without a third party agreeing.

Take Osama Bin Laden for instance, were we right in going after him? He was never a US resident.

If they are a threat to the United States (Terrorists, bombers, etc.), and if they have murdered citizens of the country illegally, then I personally don't care where they are. The CIA has the right to find and exterminate any terrorists or federal criminals, wherever they might be, and kill/arrest them.

CIA is situated from the U.S. If they wish to handle foreign situations, they need permission from legal authorities in which the CIA's foots are under.

In other words, nope.