In a bowl, mix together the olive oil, red wine vinegar, parsley, garlic, oregano, salt, and black pepper to make the chimichurri sauce.
Reserve half of the chimichurri sauce for serving and use the remaining half to marinate the chicken.
Marinate the chicken breasts in the chimichurri sauce for at least 30 minutes or up to 4 hours in the refrigerator.
Heat a grill to medium-high heat. Grill the chicken for about 4-6 minutes on each side, or until the chicken is cooked through and has grill marks.
Remove the chicken from the grill and let it rest for a few minutes before serving.
Serve the grilled chicken with the reserved chimichurri sauce.