I wasn't able to find much information about this old cemetery and chapel other than it dates back to 1836, the original chapel was destroyed in a storm and was rebuilt in 1868.
The entry on findagrave.com has photos of this cemetery but describes a different Asbury Cemetery in Anderson Township. You will find that many Methodist Cemeteries are named "Asbury" after Francis Asbury, one of the first two bishops of the Methodist Episcopal Church in the United States