Heat the oven to 425°F. Combine the eggplant, zucchini, squash, tomatoes, onion, garlic, salt, and thyme in a large roasting pan. Drizzle with the oil and toss to combine.
Transfer to the oven and roast, stirring occasionally, until the vegetables are lightly browned and tender and some water has released from the tomatoes to create a sauce, 30 to 40 minutes.
Add the chickpeas, stir, and return to the oven until the beans heat through, 5 to 10 minutes. Add the basil and stir. Taste and adjust the seasoning and serve hot, warm, or at room temperature.