Bring a large pot of water to a boil and cook the stalks until very tender, 18-20 minutes, and drain.
Place the garlic in a food processor and pulse until chopped. Add the chard stalks and puree, then add the remaining ingredients and process until very smooth.
Transfer to a shallow bowl, drizzle with olive oil, and serve at room temperature. The hummus can be stored in the refrigerator for up to 3 days.