Sprinkle chicken with salt and pepper. Melt 2 tablespoons butter in large non-stick skillet over medium heat. Add chicken to skillet and sauté until golden brown, but not cooked through, about 2 minutes per side. Transfer to plate.
Add onions, garlic, bay leaves and thyme to same skillet and sauté until onions are very tender, about 10 minutes. Add broth, wine, and bring to a boil. Boil until liquid is reduced by half, about 6 minutes.
Return chicken to skillet and turn to coat with wine mixture. Reduce heat to low; cover and simmer until chicken is cooked through, about 4 minutes. Transfer chicken to platter; cover with foil.
Strain sauce into bowl and reserve half of onions (discard remainder). Return sauce and reserved onions to same skillet. Bring to simmer and reduce once more until liquid is reduced by half.
Remove from heat and add remaining 2 tablespoons butter. Whisk until melted. Season with salt and pepper. Spoon onion mixture over chicken.
This exquisitely delicious recipe is one of the most satiating meals made with chicken. Thanks to the abundance of quality fat in this dish, dessert will not be necessary! Fat soluble vitamins A, D and E can be found in this dish alongside abundant amounts of protein. The garlic and onions also stimulate immune function… and just plain taste delicious!