Heat water for pasta and begin to cook it according to package directions.
While the pasta is cooking, wash the chard and remove the stems; set them aside for another use. Chop the leaves coarsely.
Over medium-high heat, heat a large non-stick pan. Add the onion and sprinkle it lightly with salt. Cook, stirring, until onion begins to brown. Add garlic, red pepper flakes, and mushrooms and reduce heat. Cook, stirring, until mushrooms soften, adding a tablespoon or two of water if needed to prevent sticking. Add tomato paste and water and stir to combine. Add chickpeas and simmer until pasta is done.
When pasta is cooked, remove and reserve 1 cup of the cooking liquid before draining. Add 1/2 cup of the liquid to chickpeas and mushrooms. Stir in the chard and cover. Cook until chard is just wilted, about 2-3 minutes. Stir in the pasta, add additional pasta water if necessary to moisten, and add salt and pepper to taste. Just before serving, stir in orange juice or balsamic vinegar.