Get ready: Preheat your oven to 425°F.
Turn the chicken breasts into cutlets so they cook quickly and more evenly. Use a sharp knife to cut each chicken breast horizontally into two halves, starting on the thicker end and carefully slicing your way to the thinner end. Place the chicken breast halves, one at a time, in a large bag and zip the top shut (make sure to release the air before closing the bag). Use a meat mallet or the back of a heavy cast iron skillet to pound the chicken flat. You want each breast to be about ¼-inch thick all over.
Season the chicken. In a small bowl, mix together the oregano, thyme, paprika, and a large pinch of salt and pepper (about ½ to ¾ teaspoons each). Pat the chicken dry and season on both sides with the spice mixture.
Make the sauce. In a large oven-safe pan with a lid, melt the butter over medium-high heat. Add the olive oil and wait for it to shimmer. Add the garlic and cook, stirring regularly, until fragrant, about 30 seconds. Now add the wine and cook briefly to reduce by half, then add the lemon juice and capers. Turn the heat off.
Bake. Add the chicken and artichoke hearts to the pan and spoon some of the sauce on top. Cover the pan and transfer to middle rack of your heated oven. Bake covered for about 10 minutes, then uncover and bake for another 5 to 8 minutes or until the chicken breast are fully cooked through and no longer pink in the middle.
Finish and serve. Garnish with the parsley and lemon zest and serve immediately.
