Preheat over to 450 degrees.
Combine the two grated cheeses and press 1/2 cup of the mixture into the pie shell. Chill. Mix the rest of the cheese with the breadcrumbs and set aside.
Wash the zucchini and cut them into 1/4-inch slices, making them as even as possible. Drop them into a kettle of boiling salted water for 2-3 minutes, then drain and chill.
Beat together the egg yolks and the sour cream. Add the chives, flour, salt, and pepper. Beat the egg whites with the cream of tartar until they are stuff but not dry, then fold them into the sour cream mixture.
Arrange a layer of zucchini slices on the bottom of the pie crust, placing them edge to edge and cover with a small amount of the sour cream mixture. Continue with these layers until the zucchini slices are all used up. Cover the top with the remaining sour cream mixture. Sprinkle over it the cheese and breadcrumbs, then dot with slivers of butter.
Bake for 10 minutes in the 450-degree oven, then lower the temperature to 325 degrees and bake for an additional 40 minutes. Serve warm.