Preheat oven to 375 degrees. Whisk together egg, whites, ricotta, teaspoon salt, and the pepper in a medium bowl.
Heat oil in a 10-inch ovenproof skillet over medium-high heat. Add Swiss chard stalks and onion, and cook until onion is tender and translucent, about 4 minutes. Add Swiss chard leaves, and cook, stirring, until tender, about 1 1/2 minutes. Sprinkle with remaining 1/4 teaspoon salt. Add egg mixture, and stir once or twice to distribute vegetables evenly. Place skillet in oven, and bake until eggs have set, about 13 minutes. Serve immediately.