The Greek island known for the mastic resin used to flavor foods and liqueurs is Chios.
Chios is especially famous for mastiha, the aromatic resin of the mastic tree, Pistacia lentiscus var. chia. The resin is harvested mainly in the island’s southern villages, collectively known as the Mastichochoria. Growers make incisions in the bark, allowing translucent resin “tears” to harden on the ground before collection and cleaning.
Mastic has been valued since antiquity as a flavoring, breath freshener and ingredient in sweets. In Greek cuisine it can perfume desserts, chewing gum, breads and ice cream. Its pine-like, herbal aroma also gives Chios mastiha liqueur its distinctive character; that drink is traditionally served chilled, often after a meal.
The island’s association is unusually specific because comparable mastic trees grow elsewhere around the Mediterranean, but Chios mastiha has a long-established cultivation tradition and protected geographical status. Thus “Chios” is the canonical answer, rather than a larger Greek island associated with general regional cuisine.