Preheat oven to 350. Combine potatoes, sour cream, milk, cheese and chives in medium bowl. Spoon into buttered shallow 2-qt rectangular casserole. Bake 40 minutes. Cut sausage into halves lengthwise, then cut crosswise into bite-sized pieces. Arrange down center of casserole. Bake 10 minutes more. Shape a well in each corner of the potato mixture. Break an egg into each well. Bake 10 to 12 minutes more or until eggs reach desired doneness. Serve immediately.