Drain the beans and put in a saucepan. Cover with water and bring to the boil with the carrots, onion, garlic and 3 tablespoons of the olive oil. Simmer for 2 hours.
Add the salt and simmer for a further hour until the chickpeas are cooked. Add water if necessary to keep them covered.
Drain, reserving the liquid, but discarding the carrot, onion and garlic. Serve the chickpeas hot with a little of the liquid, a teaspoon of vinegar, the remaining olive oil and a sprinkling of pepper.