Bring goat milk in a heavy bottomed pot to the boil over medium heat. Take off the heat. Immediately stir in the lemon juice into the milk. Leave standing for about a couple of minutes, so the milk can curdle. Pour the milk lemon mixture into the cheese cloth (or alternatively a clean kitchen cotton towel), that has been laid out in a bowl. Tie the ends of the cloth together so it becomes a bag. Hang it on a wooden spoon and let the bag hang free. The whey should be able to strain out of the cheese cloth for at least two hours.
Before taking the cheese out of the cloth, you can squeeze the cloth itself to extract more liquid from the cheese. Transfer the cheese from the cloth to a bowl, season it with salt and pepper and fresh chives. Ready to serve.