Place the chicken on the prepared baking sheet. Drizzle lightly with the olive oil and sprinkle with salt and pepper. Roast until golden and completely cooked through, about 50 minutes. Cool completely.
Remove the skin from the chicken. Shred the meat with a fork and then roughly chop. Add to a bowl with the grapes, mayonnaise, chives, lemon juice, celery, and salt and pepper to taste and mix well. Divide the chicken salad among the toast cups.