1. Find wood shipping pallet.
2. Strap chair securely to same.
3. Wrap liberally in poly wrap (think industrial Saran Wrap).
4. Call freight company or moving companies for quotes (get weight estimate before calling).

My company regularly ships 150 lb packages across the US via Yellow Freight. Our rates are about $50 on one side of the Mississippi and $85 to the other side.

HTH.

-Zeke