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Hi, I am Dr. Peter and would like to help.
1- Is it limited to her chin or has other lesion elsewhere?
2- Is she itchy?
Seems that she may have what is called "Feline Acne." The black scabs are what is called "comedons (black heads)." The cause is unknown, there are theories where it may be associated with stress or allergies. You can treat by cleaning the area with a benzoyl peroxide gel or shampoo (antiseborrheic shampoo). If it becomes very inflamed or infected may need a short course of steroids and oral antibiotics. Try first to treat it with the benzoyl peroxide. If no improvement within a week then have her checked by your veterinarian.
If you have additional questions I will be glad to answer them.
If these are scabs then this could be an allergic contact dermatitis, if you have plastic bowls switch it to metal. Or, it is a localized bacterial infection. You can use the benzoyl peroxide to clean followed by a topical antibiotic like neosporin.