"It's pretty much fruitless to generalize about the food supply of a whole country. "
You're probably looking for someplace too poor to afford to use pesticides and such. Small(er) farms. A lot more subsistence farming. Any place that can do larger scale can do chemicals. Perhaps borders to transport (like Islands) keep farms small as well.
Puerto Rico, Dominican Republic, Caribbean Islands, and (as has been mentioned) Mexico, come to mind. But even there it's going to vary. Just possible you can find areas. Posts here about Oaxaca Mexico seem like that might fit.
Or perhaps you could contact organizations like Organic Farming standards and ask if there are communities that practice such. Religious organizations like (IIRC) Seventh Day Adventists, Jehovah Witness, others have long had fairly strict vegetarian diets and might know of communities like that in this country.
Good luck!