They are a delicacy in many of the Carribean islands. A few years ago I was reading that there was a shortage in some of the areas and they had to import them from other islands.
I worked with a guy who had a Pet iguana and brought in a picture. Another co-worker who grew up in Trinidad was very interested, claimed they were very good to eat. The picture was quickly put away :)
they are also eaten in central america where they are called tree chickens (in their native language.)