Whisk first 5 ingredients in a small bowl. Gradually whisk in oil. Season to taste with salt and pepper. Stir; set aside. Remove crispy chicken skin and tear into pieces. Pull chicken meat from bones and tear into pieces; discard bones. Reserve skin and meat.
Heat chicken fat in a large skillet over medium heat. Add bread to skillet and toast, turning frequently, until golden and crisp, about 2 minutes. Remove with a slotted spoon and drain on paper towels. Season with salt and pepper while still hot.
Place chicken meat in a large bowl. Add cherries, butter lettuce, radishes, and chives and drizzle with vinaigrette; toss to coat. Divide salad among plates and garnish with croutons and chicken skin.
Calories 705 Fat 40 g Carbs 48 g Nutritional analysis provided by Bon Appétit