Bring a medium pot of salted water to a boil. Add the chard and cook for 3 minutes. Drain thoroughly and set aside.
In a Dutch oven, heat the oil over moderate heat. Add the potatoes and onion and sauté, stirring frequently, until the potatoes start to brown, about 5 minutes. Add the garlic, paprika, turmeric, cayenne, and salt and cook, stirring, until fragrant, about 1 minute.
Add the cooked chard, chickpeas, broth, and water. Bring to a simmer and cook until the potatoes are tender, about 15 minutes.