Colonists on a new world are concerned that there don't seem to be many species of plant or animal that they can digest.
They finally find one (shrimplike?), but it seems to be rare, and they are not sure if there will be enough local food available to make continuing the colony worth it.
The local aliens really want them to stay, so hunted down every last one of the human-edible species to give to the humans for a friendship feast.
The humans discovered that in one night they had eaten the one digestible local species to extinction. The local aliens thought that the loss of this species was worth it, as it would bind the colonists to them, meaning they would never leave.
Edit: I believe it was in a short story collection, and that I read it at least 10 years ago. Could be a lot older than that, though.