1796, originally "Irish," now "pertaining to the Gaels" in the broadest sense; a "discriminated form" [Century Dictionary] of Gaelic.
Entries linking to gadhelic
Gaelic adj.
1774, "of or pertaining to the Gaels" (meaning originally in English the Scottish Highlanders); 1775 as a noun, "language of the Celts of the Scottish Highlands;" earlier Gathelik (1590s), from Gael (Scottish Gaidheal; see Gael) + -ic.