Prepare the chicken: If not already cooked, poach, bake, or roast chicken breasts or thighs until just cooked through. Let cool, then chop or shred into bite-sized pieces.
Hard-boil eggs: Place eggs in a pot of cold water, bring to a boil, then cover and let stand off heat for 10–12 minutes. Cool under cold running water, peel, and chop.
Make the dressing: In a small bowl, whisk together the mayonnaise, sour cream (if using), Dijon mustard (if using), lemon juice (if using), salt, and black pepper until smooth.
Combine ingredients: In a large mixing bowl, add the chopped chicken and hard-boiled eggs. Pour the dressing over the top.
Mix: Gently fold everything together until the chicken and eggs are evenly coated. Stir in fresh herbs if using.
Taste & adjust: Taste the salad and adjust seasoning with more salt, pepper, or lemon if desired.
Chill: For best flavor, refrigerate for at least 30 minutes before serving.