Wash the Swiss chard; cut off stems, dice finely, and set aside.
Chop the leaves.
Heat 1 tablespoon olive oil in a nonstick 9-inch skillet with an ovenproof handle. Add onion, ¼ teaspoon of salt, and rosemary. Sauté 10 minutes over medium heat, until the onions are very soft and just starting to brown.
Stir in the Swiss chard leaves and the remaining ¼ teaspoon salt, and sauté 1 to 2 minutes, or until the greens are just wilted. Remove from heat, stir in garlic and Swiss chard stems, and set aside.
Whisk eggs in a bowl. Add the Swiss chard mixture and goat cheese, and stir to combine.
Wash and dry the skillet and return to stove top.
Preheat the broiler unit in the oven.
Heat the remaining tablespoon oil in the skillet over medium-high heat. When the oil is very hot, pour in the vegetable-egg mixture and cook for 3 to 4 minutes, or until the eggs are set on the bottom.
Transfer the skillet to the preheated broiler and broil for about 3 minutes, or until the frittata is firm and golden on top.
Loosen the frittata from the skillet and invert onto a large round plate. Cut into wedges and serve.