Combine all the marinade ingredients in a large container and add the chicken breasts; toss to cover and refrigerate for 2 hours (or overnight).
Preheat the oven to 375°F.
Heat a grill pan or large skillet on high heat and add the marinated chicken. Cook for about 2 minutes per side, until grill marks appear. Place the pan in the oven (or use a baking sheet) and roast for 15 to 18 minutes, or until the internal temperature of the chicken reaches 160°F.
Transfer the chicken breasts to a cutting board, tent with aluminum foil, and let rest for about 5 to 10 minutes before slicing 3/4-inch thick.
Meanwhile, combine the chickpeas, olive oil and dill in a bowl and set aside.
In a large mixing bowl, toss together the lettuce, kale, and cabbage and divide between 4 serving plates. Arrange the sliced chicken breasts, chickpeas, cucumber, tomatoes, feta, and olives on top and scatter the mint over the salad.
Blend or whisk together all the dressing ingredients and season to taste. Serve on the side or on top.