In a bowl, mix sour cream, lemon peel, and 1 tablespoon lemon juice. Gently stir in crab, chopped chives, and bell pepper. Add salt and pepper to taste.
Cut avocados in half lengthwise; remove pits. Brush all cut surfaces of the avocados with remaining 1 tablespoon lemon juice.
Set each avocado half, cut side up, on a salad plate; if necessary, cut a strip off the bottom of each, through peel, to balance. Mound crab salad equally in cavities. Garnish with anchovy fillets, lemon wedges, and whole chives. Add more salt and pepper to taste.