Whisk the buttermilk and half of the hot sauce in a large bowl. Season with salt and pepper. Add the chicken and marinate, covered, in the refrigerator, for about 45 minutes to 1 hour.
Meanwhile, prepare the slaw. Combine the mayonnaise, sour cream and blue cheese in a food processor or blender and process until smooth. Season with the remaining half of the hot sauce and salt and pepper. You should have about 1 cup dressing. Just before cooking the chicken, toss the cabbage, carrots and celery with about 3/4 cup of the dressing. Reserve the remaining 1/4 cup dressing for serving.
Put the cracker crumbs in a shallow bowl or plate. Lift the fingers 1 at a time and drain off the excess liquid. Dip into the crumbs and turn to coat on all sides.
Heat half the oil in a large skillet over medium-high heat until hot but not smoking. Add half the chicken and cook, turning once or twice, until browned and cooked through, 6 to 8 minutes. Repeat with the remaining oil and chicken.
For your picnic, package the reserved dressing, slaw, and chicken.
Recipe courtesy of Sara Moulton, Sara Moulton Cooks at Home, Broadway Books, 2002