Pat the chicken breasts dry, sprinkle with salt and pepper. Heat oil in a skillet, and cook the chicken in the oil over medium-high heat until firm to the touch, 4 to 5 minutes per side. Remove the chicken and keep warm on a plate wrapped with foil.
MAKE THE SAUCE:
In the same pan, combine the butter, onion, mushrooms, and thyme and cook over medium heat, stirring occasionally, 5 minutes. Add the Madeira wine and cook until almost all of the liquid is absorbed, 2 minutes. Stir in the cream, salt and pepper. Add the chicken to the mushroom sauce in the pan, and continue cooking until the sauce is slightly thickened, 3 to 5 minutes. To serve, spoon the sauce over the chicken.