Heat oil in a skillet and sear chicken breasts until they are golden. Place chicken breasts in an ovenproof pan and finish cooking them in a preheated oven to 400ºF (200ºC) until done, approximately for 10 - 15 minutes.
While chicken is in the oven, melt butter in a skillet and add onion. Cook onion until transparent not browned. Stir in wine and bring to a boil, approximately 3 minutes. Add chicken stock and heavy cream and boil for 10 minutes. Season with salt and pepper. If a thicker sauce is desired, dissolve 1 tablespoon flour in 1/3 cold water and stir in to boiling mixture.
Add chopped basil and combine to mix. Correct seasoning.
Serve basil sauce over chicken breasts.
Preparation time: 45 minutes