Place 1 piece of chicken between 2 sheets of plastic wrap. Use a meat mallet or rolling pin to gently pound until 1.5cm thick. Repeat with the remaining chicken. Season well.
Heat a large flameproof roasting pan over high heat. Melt 20g of the butter in the pan. Add the chicken to the pan and cook for 2 mins each side or until the chicken is golden brown and just cooked through. Transfer to a large heatproof plate and cover with foil. Reduce heat to medium.
Place remaining butter in the pan and cook, stirring, for 2-3 mins or until the butter melts and is golden brown. Add the garlic and capers to the pan and cook for 1 min or until the capers are crisp. Add the lemon zest and lemon juice and stir to combine. Return the chicken and any juices to the pan. Cook, turning occasionally, for 2 mins or until the chicken is cooked through and the sauce thickens slightly.
Meanwhile, place the tomato, onion, olive and fetta in a bowl and gently toss to combine.
Sprinkle the chicken with the tomato mixture and parsley and serve immediately.