Preheat oven to 350.
In small plastic container, add the olive oil and balsamic vinegar. Shake in a few dashes of salt and pepper. Close the container and shake vigorously, until well combined.
In 8x8 baking dish, place the chicken breasts snuggly into the dish. Add the sliced onions on top. Pour the balsamic vinaigrette over the chicken and the onions.
Bake at 350, uncovered, for 50-60 minutes, or until chicken is no longer pink in the middle. Cooking time may vary depending on thickness of the chicken breast.
In a small saucepan, cook 1 cup of rice according to package directions.
Steam broccoli in stovetop steamer or in a microwavable dish with 1/4 cup of water, covered in plastic wrap for 4-5 minutes.
Serve Balsamic Chicken with Onions, Steamed Rice and Broccoli.