Core the apples, peel them and cut them into 1/4 inch thick slices. Rub them with the lemon to prevent discoloration.
Melt 1 Tablespoon of butter in a skillet and saute the apples over medium-low heat, 5-7 minutes. Sprinkle them with sugar, raise the heat and cook over high heat until lightly browned on all sides, shaking the pan to prevent scorching. Set the apples aside.
Slice the chicken breast in half where the are thickes to make very thin breasts. Melt 1 Tablespoon butter in a large skillet. Raise the heat to high, add chicken and cook about 2 minutes each side. Remove chicken and set aside covered.
Add chopped onion to the skillet, cover and cook on low until it is tender and slightly caramelized, 8-10 minutes. Uncover, raise the heat to high and add the vinegar. Cook the mixture down to a syrup, about 1 minute. Whisk in cream, stock and salt.
Return chicken to the skillet and simer gently in the sauce, basting often, until the sacue ahs thickened and the chicken is cooked, 3-5 minutes. Do not overcook.
Remove chicken with a slotted spoon. Add apples to the skillet; cook over high heat until the sauce has recuded and the apples are thoroughly heated, about 1 minute.
Spoon apples around chicken and pour the sauce over and serve immediately.