Start to finish: 45 minutes
Hands on time: 45 minutes
1 pound chicken breast cutlets, preferably thin sliced
1/4 cup plus 1 tablespoon vegetable oil, divided
3 tablespoons rinsed, drained and dried capers
Kosher salt and freshly ground black pepper
All-purpose flour (preferably wondra) for dredging the chicken
1 lemon sliced very thin crosswise
2 tablespoons sugar
2 tablespoons minced shallots
1 1/4 cups chicken broth
Working with 1 cutlet at a time, place the chicken in a resealable plastic bag, add a few teaspoons of water and pound the chicken in the bag, using a meat pounder or rolling pin, until it is 1/8-inch thick. Transfer to a plate and repeat the procedure with the remaining chicken. Cut the pounded chicken in half if the slices are too large to sauté easily. Pat the chicken dry.
In a large skillet combine the oil with the capers, turn on the heat to medium high and cook the capers, stirring, until they are crispy, about 2 minutes. Transfer the capers to a small bowl with a slotted spoon. Remove the skillet from the heat while you prepare the chicken.
Working with half the chicken at a time, season the chicken on both sides with salt and pepper and dip it in the flour, shaking off the excess. Heat the skillet over medium high heat, reduce the heat to medium and add the chicken. Cook until lightly golden, about 2 minutes a side. Transfer the cooked chicken to a plate.
Season and flour the remaining chicken and sauté it in 2 tablespoons of the remaining oil, transferring the chicken as it is done to the plate.
Dip the lemon slices in the sugar, coating them lightly on both sides and add them to the skillet. Cook over medium heat, until they are lightly caramelized, about 1 minute a side. Transfer them to the plate with the chicken, add the remaining tablespoon oil and the shallots to the pan and cook stirring, 1 minute.
Add the chicken broth and bring it to a boil, scraping up the brown bits in the bottom of the pan. Return the chicken and lemon slices to the pan, along with any juices from the plate the chicken was on and simmer very gently, turning the chicken over several times, until the chicken is heated through.
Transfer the chicken to plates and simmer the sauce until it has thickened.
Spoon the sauce and lemon slices over the chicken and top with the fried capers.