Preheat oven to 350 degrees. Lightly oil a baking sheet; set aside. Season chicken with salt and pepper, and place on prepared baking sheet. Place in oven, and bake until cooked through, 30 to 40 minutes. Remove from oven, and let cool. Cut into large pieces, transfer to a food processor, and pulse until coarsely ground.
Meanwhile, fit a stockpot with a steamer basket, and add 2 inches of water. Add Swiss chard and cook until wilted. Remove, and let cool. Coarsely chop; set aside. You should have about 2 cups.
In a large bowl, combine chicken, Swiss chard, ricotta cheese, Parmigiano-Reggiano cheese, eggs, white pepper, and nutmeg. Season with salt.
If using a ravioli board; sprinkle with flour. Lay pasta sheets over board to cover. Place one teaspoon of filling into each depression. Lightly brush exposed dough with water. Lay remaining sheets of pasta over filling to cover. Press gently with hands to seal. Using a rolling pin gently roll over ravioli to seal completely. Turn out onto work surface. Using a serrated pastry wheel, cut into individual ravioli.
If you are not using a ravioli board, cut a single sheet of pasta at a time into rectangles 2 inches by 1 inch. Place a teaspoon of the chicken mixture into the center of each rectangle and fold the pasta to form a 1-inch square, pressing the edges to seal. Repeat, using all of the ingredients.
Bring a large pot of salted water to a boil. Working in batches, cook the ravioli, until it floats to the top and is cooked through, about 2 1/2 minutes. As each batch is cooked, transfer to a large platter, and keep warm.
Top with pasta sauce, and garnish with cheese. Serve immediately.