I don't know how reliable this site is, but I thought I would share these links:

Chicago to Belize City, BZ from $348 - Save $110

St Louis, MO to Belize City, BZ from $348 - Save $251

It says that these fares are "new" and may not been added to online booking sites (Travelocity, Expedia, etc). I have not been able to find these deals yet but will keep looking. If anyone else find anything, please let us know!