In a medium bowl, combine the parsley, olive oil, red wine vinegar, garlic, red pepper flakes, oregano, salt, and pepper. Mix well to create the chimichurri sauce. Set aside about half of the sauce for serving later.
Place the chicken breasts in a large resealable plastic bag or shallow dish. Pour the remaining chimichurri sauce over the chicken, ensuring it is well coated. Seal the bag or cover the dish and marinate in the refrigerator for at least 1 hour, or up to 4 hours for more flavor.
Preheat your grill to medium-high heat. Remove the chicken from the marinade and discard the marinade.
Grill the chicken for 6-7 minutes on each side, or until the internal temperature reaches 165°F.
Remove the chicken from the grill and let it rest for 5 minutes before slicing.
Serve the grilled chicken with the reserved chimichurri sauce drizzled on top and lemon wedges on the side.