Heat the olive oil in an 8-inch skillet over medium high heat, and swirl to cover the bottom of the pan. Add the chicken breasts and sear them until browned. Turn the chicken, and brown them on the other side. Remove the chicken breasts to a plate and increase the heat to high. Deglaze the pan with the lemon juice, scraping up any browned bits into the sauce.
Add the stock and bring to a simmer. Add the lemon slices to the pan, reduce the heat to medium, and place the chicken breasts on top of the lemon slices. Add the capers, cover, reduce the heat to medium and cook, covered, for 10 minutes. Remove the lid and add the drained artichoke hearts. Cover and continue cooking for five minutes, or until the breasts are cooked through.
Remove the chicken to a warm plate. Increase the temperature and reduce the sauce to a glaze. Taste the sauce and adjust the seasoning with salt and pepper as needed. Just a little salt will reduce the acidity of the lemons, capers and artichokes and balance the flavors. Serve the chicken with the artichoke hearts, capers and melted lemons drizzled with the glaze.