Add 1 tablespoon of olive oil to a large pan over medium high heat. When the oil is hot , add the chicken and brown on both sides.
Remove the chicken from the pan. Lower the heat to medium and add 1 tablespoon olive oil, mushrooms, shallot and garlic. Cook until the mushroom cook down a bit.
Add the wine, juice of one lemon and salt and pepper. Let that cook together for a minute or two.
Add the chicken back to the pan and cook until the chicken is cooked through- about 10 minutes. Cover the pan if needed.
While the chicken is cooking slice the remaining lemon into round slices.
Remove the chicken to a serving platter. To finish the sauce, add 2 tablespoons of butter to the pan along with lemon slices and drained capers.
Cook for a few minutes to let the flavors get happy.
Pour the sauce over the chicken.