Trim any dark brown areas from the smoked salmon, and use to line 8 small ramekin dishes so that it is overhanging the edges of the moulds. Whisk together the eggs, chives, salt and pepper.
Melt the butter in a heavy-based non-stick pan, add the eggs and cook over a medium heat, stirring constantly with a wooden spoon so the eggs do not stick. When they are nearly set, remove from the heat and add the cream to stop them cooking any further. Continue stirring for 30 seconds.
Fill the lined ramekins with the scrambled eggs and fold over the smoked salmon overhanging the sides. Turn out of the ramekins onto heatproof serving plates and place briefly under a pre-heated grill to just warm the smoked salmon.