In a medium bowl, combine the tomatoes, garlic, oregano, 1/2 teaspoon salt, and 1/2 teaspoon pepper.
In another medium bowl, combine the ricotta, parsley, Parmesan, and 1/4 teaspoon pepper.
Spoon 1/3 cup of the tomato mixture into the bowl of a slow cooker. Top with a single layer of noodles, breaking them to fit as necessary. Add half the Swiss chard. Dollop with a third of the ricotta mixture and a third of the remaining tomato mixture. Sprinkle with a third of the mozzarella. Add another layer of noodles and repeat with the other ingredients. Finish with a layer of noodles and the remaining ricotta mixture, tomato mixture, and mozzarella. Set the slow cooker to low and cook, covered, until the noodles are tender, 2 to 3 hours.
If You Don't Have a Slow Cooker: Heat oven to 375° F. Follow the recipe above using no-boil lasagna noodles in place of the dried ones and layer the ingredients in a Dutch oven or large casserole. Cover and bake until the noodles are tender, 50 minutes to 1 hour.
This recipe was tested in a 6-quart slow cooker. Because different models cook at different rates, the cooking time below is presented as a range. Check for doneness at the low end of the range (but not before, as the escaped heat will significantly slow the cooking). If the food is not done, cover and cook to the end of the suggested time range. If using a slow-cooker smaller than 6 quarts, the cooking time may take an additional hour or more, and results may vary.