Preheat oven to 375 degrees F.
Mix together the chopped cheese, Canadian bacon, and chives and season with a few grinds of pepper. In a bowl, beat the eggs. Brush the muffin tins with melted butter. Using a teaspoon, fill the 24 mini-muffin cups halfway with the cheese mixture. Using a ladle, fill the cups to just below the edge with the beaten eggs. Bake until golden, about 12 minutes. Remove and let cool to handle, then arrange the egg bites on a plate and serve.