Heat oven to 375°F. In 4-quart saucepan, mix filling ingredients. Cook over medium heat, stirring occasionally, until mixture is bubbly and hot. Spoon into ungreased 13x9-inch (3-quart) glass baking dish.
In 2-quart saucepan, heat water to boiling. Remove from heat. Add milk. Stir in potato mix (dry) and ranch dip mix with fork until moistened. Let stand 1 minute. Add egg; blend well. Cool 5 minutes. Spoon or pipe potato mixture around edges of hot chicken mixture.
Bake 25 to 30 minutes or until potatoes are set and light golden brown.