Snip the tomatoes into bite-size pieces. Melt the butter in a saucepan over low heat; add the garlic and cook for 30 seconds. Add 3/4 cup of the stock and the tomatoes. Bring to a boil. Reduce the heat and simmer, uncovered, over medium heat 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. (The sauce can be kept, covered, for 1 day in the refrigerator. Heat again over low heat.) Sprinkle the chicken with salt and pepper on both sides. Heat the oil in a large, heavy skillet over medium-high heat. Add the chicken and saute, pressing on the chicken occasionally with a slotted spatula, for about 4 minutes per side or until the meat feels springy and is no longer pink inside (cut to check). Transfer to a board; cover and keep warm. Discard the fat from the skillet. Add the remaining stock and bring to a boil, stirring up the pan juices. Boil to reduce slightly, then add to the sauce. Stir in the basil. Taste and adjust the seasoning. Meanwhile, cook the pasta, uncovered, in a large port of boiling salted water over high heat, stirring occasionally (about 1 to 2 minutes for fresh or 3 to 5 minutes for dried fettucine), or until tender but firm to the bite (al dente). Drain, transfer to bowl and toss with 3 or 4 tablespoons of the sauce. Cut each chicken breasts into 2 or 3 diagonal slices. Reheat gently in the sauce if needed. Transfer the pasta to serving plates, top with the chicken and coat with sauce.