In a large oven safe skillet, heat 4 tablespoons olive oil over medium heat. Add onions, stir to coat with olive oil. Sprinkle with a pinch of salt. Cook onions, stirring occasionally to avoid burning until onions are tender and slightly caramelized, about 15-20 minutes. Stir in balsamic vinegar, cook for 1-2 minutes more. Place cooked onions in a bowl, lightly cover and set aside.
In the same skillet, over medium heat add remaining 2 tablespoons olive oil. Add chicken, season with 1/2 teaspoon salt, 1/4 teaspoon pepper, and 1/2 teaspoon thyme leaves. Cook until all sides are lightly brown and cooked through. Remove chicken from skillet to a bowl, lightly cover and set aside.
Increase heat to high. In the same skillet, add beef broth and deglaze the pan. Reduce heat to medium. Gradually whisk in flour until broth is thicken. Season gravy with a pinch salt, pepper and thyme leaves.
Stir in cooked chicken and sautéed onions until combined with beef gravy. Sprinkle with Swiss cheese and place in a 350 degree oven for about 10 minutes until cheese is melted and bubbly.
Carefully remove from the oven and sprinkle with a pinch of thyme leaves if desired.
Serve French Onion Chicken in shallow bowls over toasted baguette slices.