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.
Sprinkle the chicken with salt and pepper on both sides. In a large skillet over medium heat, warm oil and saute chicken. Press on chicken occasionally with a slotted spatula. Cook for about 4 minutes per side or until the meat feels springy and is no longer pink inside. Transfer to a board; cover and keep warm. Discard the 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 adjust seasonings to taste.
Meanwhile, bring a large pot of lightly salted water to a boil. Add fettuccine and cook for 8 to 10 minutes or until al dente; drain, transfer to a bowl and toss with 3 to 4 tablespoons of the sauce.
Cut each chicken breast into 2 to 3 diagonal slices. Reheat the sauce gently if needed. Transfer the pasta to serving plates; top with chicken and coat with the cream sauce; serve.
My Note: I marinated my chicken (6 breasts) in buttermilk for a few hours as I do with all my chicken(1cup milk 1 TBS vinegar or lemon juice if no buttermilk) for that extra moistness. Then I mixed 1/2 cup flour with 1 tbsp paprika and dredged chicken in before frying. I did it all in one skillet-why dirty more than one pan! I sauteed garlic in 4tbsp butter(instead of oil) on low heat then I raised heat to med and added chicken which I cut into strips and browned on all sides. Then I added sundried tomatoes and 1 cup mushrooms and sauteed a little longer. I followed others and doubled sauce so I added 1 cup chick broth and 1 cup white wine(for a greater flavor) salt, pepper and reduced to low, covered and cooked for 30 minutes. I removed chicken added heavy cream with 2 tbsp cornstarch(I like thicker sauce)and fresh basil and cooked to my desired thickness then added chicken back in and tossed on fettuccini.