Preheat oven to to 350 degrees F. Shed the zucchini through the large holes of the grater, then squeeze it firmly a handful at a time to extract much of the juice (which would make the dish watery if left in). Discard the juice, or add it to soup or sauce, or drink it. Toss the squeezed zucchini with the green onion and set aside. Heat the butter in a skillet over moderate heat. Toss the chicken breasts in the flour mixture, shaking off so the excess falls off, then cook them in the butter for about 3 to 4 minutes on each side, until lightly browned. Arrange the chicken in a single layer in a buttered casserole and cover each with a mound of the zucchini mixture. Sprinkle lightly with salt and pepper and cover with slices of cheese. Bake uncovered for about 20 minutes, until the cheese is lightly browned and the chicken is cooked through.
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