Fill a medium saucepan with enough water to cover the eggs and bring it to a rolling boil over high heat.
Carefully lower the eggs into the boiling water using a slotted spoon and immediately reduce the heat to a simmer.
Cook the eggs for exactly 6 minutes and 30 seconds to ensure the whites are set but the yolks remain jammy.
While the eggs cook, prepare an ice bath by filling a medium bowl with cold water and a handful of ice cubes.
Transfer the cooked eggs to the ice bath and let them sit for 3 minutes to stop the cooking process and make peeling easier.
In a small bowl, whisk together the Greek yogurt, lemon juice, sea salt, and black pepper until smooth and combined.
Spread the seasoned yogurt onto the center of a plate and scatter the fresh arugula over the top.
Gently crack and peel the eggs, slice them in half lengthwise, and arrange them over the arugula and yogurt.
Drizzle the chili crisp over the eggs and yogurt, then garnish with finely chopped fresh chives before serving.