Season chicken breasts with salt & pepper, to taste.
Heat a large skillet over medium heat then add oil & butter.
Add chicken & brown on one side, about 8 minutes, then turn over, reduce the heat & cook, covered, at least 10 minutes. Then remove breasts to a serving platter, & keep warm.
To the skillet add the chopped onion & cook until transluscent, about 5 minutes, then add the wine vinegar & turn heat to medium-low.
In a small container mix cornstarch with the tablespoon of water & mix thoroughly before adding it to the skillet, stirring to combine. Continue cooking & stirring until slightly thickened, then pour the onion mixture over the chicken breasts & serve.