TO MAKE DRESSING: Whisk the mayonnaise, spring onions, buttermilk, dill and ground black pepper in a small bowl to blend (can be made 1 day ahead). Cover and chill.
TO MAKE SALAD: Arrange the chicken in a heavy, medium size frypan. Add the wine, dill and ground black pepper. Season with salt. If necessary, add water to cover the chicken. Simmer over medium low heat until chicken is just cooked through, turning once (about 11 minutes). Transfer chicken to a plate and let cool.
Cut chicken into 1 cm pieces. Place in a large bowl. Add the grapes and the celery and mix in the dressing to thoroughly coat the mixture. Season with salt and pepper to taste. Cover and refrigerate for at least 20 minutes to develop the flavours. (Can be prepared up to 3 hours ahead).
Arrange the lettuce leaves on plates, mound on the salad and sprinkle with nuts. Garnish with fresh dill and serve.