Melt the butter in a saucepan, add the flour and cook over a low heat, stirring, for 30 seconds. Remove the pan from the heat and gradually stir in the milk until smooth. Return to the heat and cook, stirring constantly, until the mixture thickens. Cook for 1 minute.
Leave to cool slightly, then beat in the goats' cheese, egg yolks, chives, and salt and pepper to taste.
Whisk the egg whites in a large, perfectly clean bowl, until soft peaks form. Fold the egg whites into the cheese mixture. Spoon the mixture into 4 greased, individual soufflé ramekins and set on a baking sheet. Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 15–18 minutes until risen and golden. Serve immediately.