Combine the marinade: add avocado oil, balsamic vinegar, garlic, dried oregano, and sea salt to a small blender or food processor and blend until smooth.
Place the chicken breasts in a resealable container or bowl and pour the marinade over them; toss or move the chicken so each breast is well coated. Seal and refrigerate for at least 1 hour and up to 10 hours.
When ready to cook, preheat the oven to 350°F (175°C). Lightly oil or spray a casserole or baking dish and arrange the marinated chicken breasts in a single layer.
Bake on the center rack for about 30 minutes, or until the chicken reaches an internal temperature of 160°F (71°C). Remove from the oven and let rest for 10 minutes so juices redistribute.
Transfer the rested chicken to a cutting board and chop or slice into bite-size pieces.
While the chicken bakes, prepare the Lemony Caesar Salad Dressing (or use your preferred Caesar dressing) and refrigerate until ready to use.
Chop the romaine hearts and combine them in a large salad bowl with the spring green mix.
Drizzle the desired amount of Caesar dressing over the greens and toss until evenly coated.
Serve the salad in large bowls, top with the baked chopped chicken, and finish with croutons and grated Parmesan to taste.