Toss together first 2 ingredients, and place in a lightly greased 13- x 9-inch baking dish. Sprinkle with chicken and 2 cups cheese.
Melt butter in a medium saucepan over medium heat. Add tomatoes and next 8 ingredients, and cook, stirring often, 5 to 8 minutes or until tender. Remove from heat, and cool 10 minutes.
Whisk together eggs, soup, and 1 1/2 cups milk in a large bowl. Pour over bread mixture. Sprinkle with cooled onion mixture. Cover with plastic wrap, and chill 8 to 24 hours.
Pour remaining 1 cup milk over strata; top with remaining 1/2 cup cheese. Let stand 45 minutes.
Preheat oven to 325°. Bake strata 1 hour and 10 minutes or until set. Serve immediately.
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