In a medium bowl combine the dressing ingredients, including 1 tablespoon oil and ½ teaspoon salt, and whisk with a fork until blended, keeping some of the cheese lumps apparent. Refrigerate until needed.
In a small bowl whisk the sauce ingredients. Reserve 2 tablespoons for the cooked chicken.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the chicken on both sides with oil and season evenly with the paprika, pepper, and 1 teaspoon salt. Grill the chicken, smooth (skin) side down first, over direct medium heat, with the lid closed, until the meat is firm to the touch and opaque all the way to the center, 8 to 12 minutes, turning once and basting frequently with the larger quantity of sauce. Remove from the grill and let rest for 3 to 5 minutes. Cut the chicken lengthwise into thin slices. Place in a bowl with any accumulated juices. Add the reserved 2 tablespoons sauce and gently stir to coat.
In a wide salad bowl combine the lettuce, celery, carrot, radishes, and onion. Arrange the chicken in the center of the salad. Drizzle the dressing over the chicken. Garnish with the celery leaves.