How to Make It
Melt the butter in a large skillet. Add the onions and cook over moderately high heat, stirring, until softened, about 5 minutes. Add the garlic and cook for 1 minute. Add the chard and basil and cook just until wilted, about 2 minutes. Season with salt and pepper; let cool.
In a large bowl, combine the ricotta and eggs. Stir in the chard mixture and season with salt and pepper.
Preheat the oven to 375°. Place a lightly oiled rack in a very large roasting pan. Using your fingers, gently loosen the chicken skin from the breast meat. Fit a large pastry bag with a 3/4-inch round tip and fill the bag with the ricotta stuffing. Pipe the stuffing under the breast skin of each bird. Brush the chickens with the olive oil and season inside and out with salt and pepper. Tie the legs together.
Arrange the chickens, breast side up, in the roasting pan and roast fro about 1 1/2 hours, or until the skin is golden brown and the juices run clear when the thighs are pierced. Cover with foil and let rest for 15 minutes before carving.