In a large bowl, whisk together the egg yolks, chives, salt, and pepper.
In a separate bowl, with an electric mixer on medium-high, beat the egg whites until stiff peaks form. Using a spatula, gently fold the egg whites into the yolk mixture.
Meanwhile, melt the butter in a large nonstick skillet over medium-low heat and tilt to coat the sides. Add the soufflé mixture and crumble the cheese over the top. Bake until the eggs are puffed and golden, about 10 minutes. Cut into wedges. Divide the soufflé, salad greens, and tomatoes among plates. Drizzle the greens with the oil and serve with the lemon.
Tip: When you make the Skillet Soufflé, keep in mind that deflating is part of the natural life cycle of any soufflé. Though this skillet version is sturdier than the average recipe, don't be dismayed (or apologetic) when it eventually falls.