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.