Heat butter in a saucepan. Add leeks and Granny Smith apple, cover and simmer until tender, for about 5 minutes. Add the Calvados and reduce until almost evaporated. Stir in the cider vinegar, broth, apple cider and bring to a simmer.
Add the chicken and egg noodles to the broth, cover and cook until the chicken is cooked through, about 5 minutes. Skim off any fat which is floating to the surface, stir in the heavy cream, optional Gruyere and season, to taste, with salt and pepper. Garnish with chives.