In a large saucepan over low heat, melt butter; add garlic and cook for 30 seconds.
Add the tomatoes and 3/4 cup of the chicken broth; increase to medium heat and bring to a boil.
Reduce heat and simmer, uncovered, for about 10 minutes or until the tomatoes are tender.
Add the cream and bring to a boil; stirring.
Simmer over medium heat until the sauce is thick enough to coat the back of a spoon.
2Sprinkle the chicken with salt and pepper on both sides.
In a large skillet over medium heat, warm oil and saute chicken.
Cook for about 4-5 minutes per side or until the meat feels springy and is no longer pink inside.
Transfer to a board; cover with foil and keep warm.
Pour off fat from the skillet & in the same skillet, over medium heat, bring 1/4 cup chicken broth to a boil; stirring the pan juices.
Reduce slightly and add to the cream sauce; stir in basil and parmesan.Season with salt and pepper.(Be careful with salt though as tomatoes and parmesan are quite salty)
Cook Fettucini until Al Dente; drain, transfer to a bowl and toss with 3 to 4 tablespoons of the sauce.
Reheat the sauce gently if needed,and transfer the pasta to serving plates; top with chicken and coat with the cream sauce; serve.
Sprinkle green onions on top as garnish and serve with additional parmesan cheese.