Cut the shallot in very fine strips. You could use a mandolin for that.
Then cut the apple au julienne. No need to peel it.
First cut the green from the fennel and chop it up a bit. Set aside.
Cut the fennel bulb in half and remove the tough heart.
Thinly slice up the fennel. You can again use the mandolin to do that.
Make the dressing by mixing vinegar, oil, salt, pepper and a little bit of liquid sweetener.*
Mix the shallot and the fennel greens into the dressing.
Add the apple and the fennel and mix well. Let sit for about an hour.
Just before serving, cut the smoked chicken breast into small pieces or slices and mix through the salad.
*The sweetener is optional, but it lifts this dressing to the next level.