Preheat an oven to 350 degrees. Wrap each head of garlic separately in aluminum foil. Place the parcels on a rack in the center of the oven and bake for 45 minutes. Remove the garlic heads from the oven and set aside to cool slightly so that they can be handled.
In a large pot bring 6 quarts salted water to a boil. Add the fettuccine to the boiling water and cook until al dente. Meanwhile, unwrap the garlic heads, separate the cloves and squeeze the garlic cloves from their papery sheaths into a hot serving bowl. Add the olive oil and season to taste with salt.
Sprinkle with the chili and blend together well with a fork. Drain the pasta and transfer it to the serving bowl. Toss the pasta with the sauce.
Serve immediately. Serves 6.