Cut the sausage into 1/4-inch chunks. In a medium skillet over medium-low heat, brown the sausages. When brown, add the chili and heat through, about 5 minutes. For an extra-cheesy omelet, stir in a handful or 2 of the cheese.
While this is cooking, heat an 8-inch skillet over medium-low heat and melt the butter. Beat the eggs with half the chives and pour into the pan. Cook until the egg forms a solid yellow circle. Cover half of the omelet with the sausage and chili mixture, reserving 1/4 cup. Add a layer of cheese, reserving 1/4 cup. Fold the omelet and top with the remaining chili and cheese. Slide the omelet onto a plate and garnish with a large dollop of sour cream and the remaining chives.