Is it permissible to sell birds on a farm on the condition that the buyer hunts them and pays for each bird he catches?

It is not permissible to sell birds that have been hunted, due to the presence of Jahalah (ignorance) and Gharar (excessive uncertainty) in such a transaction. This is because the birds vary in value, and one might hunt something worthless. This falls under the category of buyu' al-gharar (sales involving excessive uncertainty) which are forbidden by Islamic law. It is similar to bay' al-hasah (pebble-toss sale), and this principle applies to any sale involving something unknown, non-existent, or that cannot be delivered.