Cook the chicken according to package directions.
Heat broiler. On one side of a baking sheet, place the rye bread; on the other side, place the chicken breasts, topping each with a slice of Swiss cheese. Broil, turning the bread once, until the bread is toasted and the cheese melts, 3 to 4 minutes.
Spread the bread with the Thousand Island dressing and top with the chicken and sauerkraut.