All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We have already issued Fatwa 86822 clarifying that the 'Awrah (parts of the body that must be covered in Islam) of a woman is her whole body with the exception of her face and her hands.
If by the expression 'under the chin' you mean the upper part of the neck which comes straight after the chin, then it must be covered as it is not a part of the face, because some women who are very fat show some of their body which is at the upper part of their neck that comes straight after the chin, and this must be covered.
However, if by the expression 'under the chin' you mean the portion which is part of the chin, then it is permissible to show it because the face is from the hair [the place where the hair grows] to the end of the chin.
Allaah Knows best.