Cook and shred the chicken if needed, then let it cool to room temperature.
In a large mixing bowl, stir together 1/3 cup mayonnaise and Dijon mustard until smooth.
Add the shredded chicken and toss to coat.
Add the halved grapes and chopped walnuts. Stir gently so the grapes do not break down.
Check the consistency and add more mayonnaise 1 tablespoon at a time if the salad looks dry.
Season with salt and black pepper to taste.
Cover and refrigerate for at least 2 hours before serving.
Serve cold on croissants, with crackers, in lettuce cups, or on toasted sourdough.
Notes
Cool the chicken before mixing it with mayonnaise for the best texture. Start with less mayonnaise and add more only if needed. Toast the walnuts if you have time for better flavor. Chill for at least 2 hours so the chicken absorbs the dressing and the flavors blend.