Preheat your grill to medium-high heat.
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.
Reserve half of the chimichurri sauce for serving. Use the other half to marinate the chicken. Place the chicken breasts in a large zip-top bag or shallow dish, pour the marinade over the chicken, and ensure it's well coated. Seal the bag or cover the dish and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
Remove the chicken from the marinade and discard the marinade.
Grill the chicken for about 6-7 minutes on each side, or until the internal temperature reaches 165°F.
Once cooked, remove the chicken from the grill and let it rest for 5 minutes.
Serve the grilled chicken with the reserved chimichurri sauce drizzled on top.