Preheat the oven to 350 degrees F (175 degrees C). Grease a baking sheet with olive oil.

Toss chard stems and onions with 1 tablespoon oil in a bowl; season with salt and black pepper. Transfer to the prepared baking sheet.

Bake in the preheated oven until chard stems softened and onion starting to brown on corners, about 15 minutes. Toss chard leaves with remaining 2 tablespoons oil; season with salt and black pepper. Place leaves over stem mixture; scatter feta on top.

Continue baking until stems tender, leaves begin to crisp, and feta melted and golden, about 20 minutes.