If using dried chickpeas pick over and rinse them. Put them in a Tupperware container or bowl with water to cover by 2 inches. Soak them in the fridge overnight. The following day rinse them again and then put them in a small pot with fresh water to cover by 2 inches. Bring to a boil and then simmer for 90 minutes. Reserve the cooking liquid/juices.
If using canned chickpeas rinse them with water.
In a food processor combine the soft chickpeas, ⅓ cup cooking liquid (or fresh water if using canned chickpeas), lemon juice, tahini, garlic, olive oil, and salt. Blend until smooth and add more liquid if a thinner sauce is preferred.