Reserve 2 slices of salmon for garnish. Chop the remaining salmon into very small pieces.
Whisk your eggs and cream together. Add ½ of your chopped chives and season eggs with salt and pepper.
Preheat a large nonstick skillet over medium heat. Melt butter in the pan and add eggs. Scramble eggs with a wooden spoon. Do not cook eggs until dry. When eggs have come together but remain wet, stir in chopped salmon.
Remove pan from the stove and place on a trivet.
Garnish the eggs with remaining salmon and chives and serve right out of the warm pan.