Rinse chicken and pat dry. Sprinkle lightly all over with salt and pepper. Place each breast half between sheets of plastic wrap; with a flat mallet or rolling pin, gently and evenly pound chicken to 1/4 inch thick. Peel off plastic wrap.
Pour oil into an 11- to 12-inch nonstick frying pan over high heat, tilting to coat bottom. When oil is hot, add chicken in a single layer, without crowding. When edges begin to turn white, turn pieces and cook until no longer pink in the center (cut to test), 3 to 4 minutes total. As chicken is cooked, transfer to a platter and keep warm; repeat to cook remaining breasts.
Add broth, artichoke hearts, olives, capers, lemon juice, and oregano to pan; stir, scraping browned bits free, until mixture boils. Stir in parsley. Spoon sauce evenly over chicken. Add more salt and pepper to taste. Garnish with lemon wedges.