In a food processor or high-powered blender, combine the chickpeas, tahini, ice cubes, garlic, lemon juice, and salt. Process until the mixture is smooth. Scrape down the sides of the food processor or blender, and blend until the mixture is super creamy, about 4 minutes. Add cold water, if necessary, for a thinner hummus. Taste, and adjust salt and lemon juice, to taste.