Yes. Chestnut is not a root vegetable, so it is generally allowed in a Jain diet. The key is to eat plain, clean nuts without oil, spices, or heavy processing, and to follow your local guru/maryada, especially during strict periods like Paryushan or Das Lakshan where some restrictions can be tighter.

Tradition note:

• Digambar and Śvetāmbar lay followers both typically allow nuts and dried fruits that are clean and simple, though exact practices can vary by sangh and season.
• If you are observing very strict vows, check with your guru or temple guidelines for your community.

You can read more here