I do not believe you can delete your thread. This can be both a good thing and a bad thing.
Good if issues were discussed that may not directly address your issue or sale, then those posts or informational tidbits can still be found. It also gives both buyers and sells what items are going for on the site.
Bad if your item has sold then your thread may continue to bump to the top of the page as individuals ask it the item is still for sale.
I would suggest that "edit" the thread you wish to delete. You can edit the title and any items in your posts under the thread. For instance if you sold your Freedom, make the thread title "SOLD - Selling my Freedom". The put a final post at the bottom of the thread using 72 pitch,
Just a suggestion.