Prepare the chicken: If not using pre-cooked chicken, poach or grill the chicken breast until fully cooked, then dice or shred it. Let cool slightly.
Make the dressing: In a large bowl, whisk together skyr (or crème fraîche), Dijon mustard, lemon juice, olive oil, and honey (if using). Season with salt and black pepper to taste.
Prepare the vegetables: Thinly slice the cucumber and radishes, and finely chop the dill and chives.
Assemble the salad: Add the cooked chicken, sliced cucumber, radishes, dill, and chives to the bowl with the dressing. Gently toss until everything is evenly coated.
Serve: Spoon the salad onto slices of Danish rye bread or serve alongside boiled new potatoes for a light, summery meal.