Preheat oven to 350 degrees. Grease a 7 x 11 inch baking dish.
Grate carrots and onion. In a large bowl, mix all ingredients together, except cheddar cheese, and spread into prepared baking dish.
Bake in preheated oven for 40 to 60 minutes. When kugel is nearly done, it will seem dry and edges will be browned. Sprinkle cheddar cheese on top and return to oven for about 5 minutes. To serve, cut into squares and top with sour cream and fresh chives for garnish. Makes 8 servings. Enjoy!