Place the chicken breasts between 2 pieces of plastic wrap and pound with a skillet until about 1/2 inch thick. Season with salt and pepper. Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the chicken and cook, undisturbed, until golden on the bottom, 4 to 5 minutes; turn and cook until the other side is golden, 2 to 3 more minutes. Transfer to a plate and set aside.
Wipe out the skillet and return to medium-high heat. Add the remaining 2 tablespoons olive oil; when hot, add the artichoke hearts and red onion and cook, undisturbed, until golden in spots, about 1 minute. Season with salt and pepper and continue cooking, stirring occasionally, until the vegetables are tender, about 2 more minutes. Add the garlic and oregano and cook, stirring, 30 seconds.
Return the chicken to the skillet and add the broth and olives. Bring to a gentle simmer, cover and cook until the chicken is cooked through, 4 to 6 minutes. Top with the parsley, feta, peppers and brine.
If frozen artichoke hearts aren't available, use jarred artichoke hearts. If Peppadew peppers aren't available, use jarred roasted red peppers.