Toss together the apple, red onion, vinegar, and chives in a small bowl. Let marinate at room temperature for 20 minutes.
Meanwhile, place a medium skillet over medium-high heat. Add the sausage and cook for 6 to 8 minutes, breaking up the sausage with the back of a spoon, until cooked through.
Place a large griddle over medium heat. Place the bread slices on a clean work surface. Spread the butter over one side of each slice of bread. Place half of the bread slices, buttered side down, on the work surface. Divide the cheese, sausage, and marinated apples and onions between the sandwiches, then place the remaining slices of bread on top, buttered side up.
Grill the sandwiches for 3 to 5 minutes per side, until the bread is golden brown and the cheese is melted.