Palmyra is a census-designated place in and the county seat of Fluvanna County, Virginia, United States. The population as of the 2010 census was 104. Palmyra lies on the eastern bank of the Rivanna River along U.S. Route 15. The ZIP code for Palmyra and surrounding rural land is 22963.The Fluvanna County Courthouse Historic District, Glen Burnie, Pleasant Grove, and Seay's Chapel Methodist Church are listed on the National Register of Historic Places.