From the record
“The Joel Eddins House is a hall-and-parlor log house on the grounds of Burritt on the Mountain in Huntsville, Alabama, and is the oldest documented building in the state. The house was built in 1810 near present-day Ardmore in Limestone County, Alabama, by Joel Eddins, a settler from Abbeville County, South Carolina.”
Wikipedia article Joel Eddins House, CC BY-SA 4.0.
One of 15 National Register listings published here for Limestone County · listed in 1996 · category: Building.
Sources: the Wikipedia article · the case file at the National Archives · the National Register database, National Park Service