In a medium bowl, whisk together the eggs, non-fat Greek yogurt, sea salt, and black pepper until the mixture is completely smooth with no streaks of yogurt remaining.
Finely mince the fresh chives and set them aside for the final garnish.
Heat a non-stick skillet over medium-low heat and add the ghee, swirling to coat the bottom of the pan evenly.
Pour the egg mixture into the skillet and let it sit undisturbed for about 30 seconds until the edges just begin to set.
Using a silicone spatula, gently push the eggs from the edges toward the center, creating large, soft curds.
Continue cooking slowly, stirring occasionally and keeping the heat low to prevent the eggs from drying out.
Remove the skillet from the heat when the eggs are mostly set but still look slightly wet and glossy.
Fold in the fresh chives and serve immediately while the eggs are warm and tender.