Peel carrots and cut into smaller pieces. Add to a small saucepan along with a small amount of water; cover and boil for 6 to 8 minutes or until tender; drain.
Drain and rinse chickpeas.
In a food processor, combine cooked carrots, chickpeas, tahini, lemon juice, garlic, cumin, and salt. Blend until smooth. If hummus is too thick, add water until it reaches the desired consistency.
Cover and chill for at least 1 hour or for up to 3 days.