Preheat an oven to 350 degrees F (175 degrees C). Grease a baking sheet with olive oil.
Toss the chard stems and onions in a bowl with 1 tablespoon olive oil. Season with salt and pepper to taste, and spread onto the prepared baking sheet.
Bake in the preheated oven until the chard stems have softened and the onion is starting to brown on the corners, about 15 minutes. Toss the chard leaves with 2 tablespoons of olive oil, salt, and black pepper. Sprinkle the leaves over the stem mixture, then scatter the feta cheese over top.
Return to the oven, and bake until the stems are tender, the leaves are beginning to crisp, and the feta is melted and golden, about 20 minutes.
