In a bowl, beat together the eggs and chives with some freshly ground black pepper.
Melt the butter in a small non-stick pan over a medium-low heat. When hot, add the eggs and cook gently, stirring occasionally, for 3 minutes or until softly scrambled.
Meanwhile toast and butter the bagels. When the eggs are ready, remove them from the heat and fold through the smoked salmon trimmings. Divide the bagels between four plates and spoon over the salmon and eggs to serve.