Place the chicken breasts in a small pot and cover them with water. Bring to a boil then reduce the heat to low and simmer for 20 minutes, until they're cooked through. Remove them from the pot and shred the meat using 2 forks. Let the chicken cool.
Place the shredded chicken in a large bowl. Add the celery, green onions, mayonnaise, cranberries, pecans, salt, and pepper and mix well.
Serve the cranberry chicken salad over greens, in a sandwich, or with crackers.