From the seller:
Circa 18THC. a fine Italian, French or Eiropean silk bodice with inner linen lining.In very good condition.
Last time I checked, Italy and France were both European....
Anyway, it's from between the 1760's and 1780's, which I know isn't terribly helpful. My guess would be more to the 1780's but there are examples of jumps/stays and even bodices from earlier than that with the tail in the back. Check out a bodice and petticoat set from the Kent museum to see what I mean. The Met also has a couple of jumps. However, both have the very unhelpful "18th century" label to them.
EDIT: I found out these were previously owned by the MET. :-) Here's the original photographs from their collection.