Put bread cubes in a 9- by 13-inch pan. Bake in a 350° oven, stirring occasionally, until dry and firm to touch, about 20 minutes.
Meanwhile, rinse and drain chard. Trim and discard discolored stem ends; thinly slice stems and coarsely chop leaves.
In a 5- to 6-quart pan over medium-high heat, stir sausage often until browned and crumbly, 5 to 8 minutes. With a slotted spoon, transfer sausage to pan with bread.
Measure fat in the 5- to 6-quart pan; add enough butter to make 3 tablespoons. Add onion and celery. Stir often over medium-high heat until vegetables are limp, about 10 minutes. Add chard and stir often until limp, about 3 minutes.
Combine bread mixture, parsley, sage, poultry seasoning, pepper, and chicken broth with chard mixture. Squeeze with your hands until evenly moistened. Return mixture to the 9- by 13-inch pan, spread level, and cover tightly.
Bake in a 350° oven until dressing is hot in the center, about 40 minutes (45 to 50 minutes if chilled). For a crusty top, uncover for the last 20 minutes.