The Cover Up:
Letelier's killing was part of Operation Condor, a top-secret gathering of South American despots, whose main goal was to kill dissidents and communists in their respective countries. And the U.S. supported several aspects of Operation Condor because, goddammit, we just loved killin' communists. Really, if you love what you do, you'll never work a day in your life.
Pinochet, who ordered the hit, came into power as a result of a U.S.-orchestrated coup. Henry Kissinger promised Pinochet that America would ignore his human rights violations in Chile, and it's possible that the CIA knew about the Letelier hit beforehand, because they were funneling money into DINA. That's speculation. But they certainly knew about it after the fact, and chose not to make a big deal about it.
So the United States didn't punish Chile, but what about Townley, the American who carried out the bombing? Killing Letelier wasn't his only crime: Townley was a comic-book caliber international assassin, who worked all over Europe and South America. He hired Italian fascists to shoot Bernardo Leighton. He even helped blow up an airplane, killing 78 people and the entire national Cuban fencing team.
Surely smuggling nerve gas into the country and committing terrorism on American soil was the last straw.
The U.S. granted him immunity from prosecution and a spot in the witness protection program. He's actually still alive today, and the U.S. is refusing attempts to extradite him.
If you're having a bad case of deja vu, that's because there's a character named Michael Townley in Grand Theft Auto V. In the game, Townley ... blows up a plane, steals nerve gas, gets granted immunity, and is put in witness protection. Look at that: GTA V really is educational.