Place the zucchini in a colander set over a bowl and squeeze the zucchini with your fingers until dry. Transfer to a bowl and stir in the flour, dill, chives, salt and egg to combine.
Heat the oil over medium heat in a large skillet. Using a number-18 ice-cream scoop (the equivalent of 3 tablespoons), or a scant 1/4-cup measure, place 4 to 5 mounds of zucchini mixture in the pan, flattening with a metal spatula to a 1/2-inch thickness. Cook until golden brown and cooked through, about 2 minutes per side, lowering the heat if over browning. Repeat with the remaining mixture.
Top each pancake with a teaspoon of sour cream and a dill sprig.