Heat olive oil in a heavy-bottomed pot over medium heat; cook and stir garlic until very fragrant, about 1 minute. Reduce heat to low; stir onion and bell peppers into garlic. Cover pot and cook, stirring occasionally, until onion softens, about 5 minutes. Remove lid; cook and stir until all liquid has evaporated and onion begins to brown, about 2 minutes.
Stir tomatoes into onion mixture; cover and simmer until tomatoes release their liquid, about 5 minutes. Stir tomato sauce, eggplant, zucchini, chickpeas, parsley, basil, and thyme into tomato mixture; season with salt and pepper.
Cover pot with a lid; cook until vegetables are tender, about 40 minutes. Remove lid and simmer ratatouille, uncovered, until thick, about 5 minutes; adjust salt and pepper to taste.