Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a bowl, mix shredded chicken with half of the shredded cheddar cheese.
Unroll the crescent roll dough and separate it into individual triangles.
Place half a slice of American cheese on each triangle, then add a spoonful of the chicken mixture.
Roll up each triangle, starting from the wider end, and place them on the baking sheet.
In a separate bowl, mix cream of chicken soup with milk and pour it over the rolls.
Sprinkle the remaining shredded cheddar cheese on top.
Bake for 20 minutes until golden brown and bubbly. Serve warm.