My baby is 9 months old and still has a quivering chin occasionally. It usually only lasts five to 10 seconds but it concerns me. She was delivered via a scheduled C-section at about 38 weeks after version attempts failed to turn her out of her double footling breech presentation. She was 20 inches and only 6 pounds when born and I worry that delivery was scheduled too early, since I never felt a contraction and she was so light for her length.
Many normal, healthy babies have occasional quivers, jitters, and tremor-like movements of their chins, especially in the early months and most commonly when they are crying or stressed. While it's true that there is such a thing as an hereditary chin tremor that has been associated with hearing loss, it's well worth pointing out that this dominant trait is actually quite rare.
That said, it's important that you address any ongoing concerns you may have with your baby's doctor—both about your baby's delivery and about her chin quivering. It will be helpful to provide your doctor with any additional information regarding how often the quivering occurs, what causes it, what (if anything) you (or your baby) can do to stop it, and whether any other movements or behaviors occur at the same time—all factors that can help reassure you and your baby's doctor that the quivering is normal and not the result of anything more serious.