Drain the soaking liquid from the chickpeas and place them in a saucepan with the carrot, celery, garlic, and onion.
Cover with water by 2 inches and bring to a boil.
Decrease the heat to maintain a bare simmer and cook until tender, 45 minutes to 1 hour.
When the chickpeas are tender, drain and use immediately, discarding the other vegetables; or if you wont be using them right away, transfer them and their cooking liquid to a container and store in the refrigerator for up to 4 days.