Preheat Panini maker or George Foreman grill.
Add onions to a small plate or bowl. Cook in microwave for 1 minute to soften.
In another small bowl, mix together chicken and 1 tablespoon barbecue sauce.
Spread the outside of sandwich thin, both top and bottom, with ½ teaspoon of butter on each. Split open and spread the inside of the bottom slice with 1 teaspoon barbecue sauce. On top of sauce, spread chicken. Top with onions, tomato, and cheese. Place remaining top piece of sandwich thin, butter side out.
Place in Panini maker or George Foreman grill and cook for 3-4 minutes until melted and golden brown. Remove with a spatula as the cheese oozes out a bit while cooking. I love it that way!
Eat with your hands or serve with a fork and knife.