Prepare the marinade by mixing olive oil, lemon juice, garlic, oregano, salt, and pepper in a bowl.
Place the chicken breasts in a resealable bag and pour the marinade over them.
Preheat the grill or oven to medium-high heat while the chicken is marinating.
Remove the chicken from the marinade and discard any leftover marinade.
Grill or bake the chicken for about 6-7 minutes per side, until fully cooked.
Remove the chicken from the grill or oven and let it rest for 5 minutes before slicing.
Garnish with chopped parsley, and serve with lemon wedges if desired.