In a large bowl, whisk eggs and cream until foamy. Melt butter in a 10-inch nonstick skillet over medium heat. Pour in the eggs and lower the heat to a low setting. Watch for the edges to just barely start to set, and then gently swipe a spatula around the edges of the pan to create large soft curds. Continue this process, pausing in between to allow time for the eggs to cook but working quickly enough so as not to overcook the eggs, just gently pushing/folding the liquid eggs to form curds. The entire process should take 8-10 minutes. Sprinkle fresh chives, and season the eggs with salt and black pepper.