Preheat grill to medium high heat. Rinse chicken breasts under warm water, pat dry with paper towel and season lightly with olive oil, salt and pepper.
In a large bowl, whisk together the buttermilk, mayonnaise, parsley, garlic, 1/2 tsp. of salt and a 1/4 tsp. of freshly ground black pepper. Grill chicken breasts over medium high heat about, 6 to 8 minutes per side or until cooked through. Remove from grill and set aside.
Add dried cranberries, sliced apples and crumbled blue cheese to homemade buttermilk dressing and toss. When plating salad, top each with sliced chicken and serve.