Near the close of the 1904 session , legislators approved the creation of Beckham County from parts of Carter , Elliott , and Lewis counties . Olive Hill was made the county seat . Soon the county 's existence was challenged in court on grounds that it fell short of the 400 square miles ( 1 @,@ 000 km2 ) required by the state constitution and that it reduced the counties it was carved from to less than 400 square miles ( 1 @,@ 000 km2 ) . Carter County joined the lawsuit , claiming the border of Beckham County passed too close to Grayson , the seat of Carter County , and Vanceburg , the seat of Lewis County . The state constitution forbade county borders to pass within 10 miles ( 16 km ) of a county seat . On April 29 , 1904 , the Kentucky Court of Appeals found in favor of the plaintiffs and dissolved Beckham County .