Place oil and onions in a saucepan, and cook over high heat for 8 to 10 minutes, until the onions are nicely browned.
Add the stock, salt, and pepper, and bring the mixture to a strong boil. Meanwhile, place the bread cubes in soup bowls and sprinkle with cheese on top. Pour the boiling stock and onion mixture into bowls and mix well. Sprinkle the chives on top, and serve immediately.