Combine olive oil, cilantro, parsley, lime juice, garlic salt, and Cajun seasoning in a large bowl. Add chicken breasts and toss to coat. Marinate in the refrigerate for at least 2 hours, preferably overnight.

Preheat an outdoor grill for medium-high heat and lightly oil the grate.

Grill chicken on the preheated grill until no longer pink in the center and the juices run clear, 10 to 15 minutes. Baste chicken with marinade as it cooks. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).