Melt the butter in a large heavy skillet over medium heat. Place the sausage in the pan and cook, stirring occasionally, until the sausage begins to brown. Distribute the sausage evenly between 4 ramekins or shallow bowls. Carefully break the eggs over the sausage. Pour the cream over the eggs and sprinkle with the grated cheese.
Set the ramekins in a pan of hot water and bake for 15-20 minutes, or until the eggs are set and the topping has begun to brown. Sprinkle with the chives and serve.