Make the marinade the night before you are serving Chicken Yassa. Combine all the ingredients for the marinade: olive oil, vinegar, lemon juice, chicken stock, garlic, ginger, salt, and pepper.
Place the chicken breasts in a bowl, baking dish, or plastic bag. Pour half of the marinade over the chicken, cover, and refrigerate overnight.
Be sure that both sides of the chicken are covered in the marinade; turn over the chicken if necessary. Save the rest of the marinade.
Turn on the broiler or prepare your grill. If using the oven, broil the chicken on the 2nd rack from the top. Cook the chicken for about 10 minutes per side, or until it is tender, basting each side of the chicken with the reserved marinade.
While the chicken is cooking, sauté the thinly sliced onions to your liking. Bring the additional saved marinade to a boil in a saucepan or microwave and simmer for 3 minutes.
Serve with the sautéed onions on top of the chicken, and the heated marinade in a pitcher, bowl or gravy boat.