Yes, I have used the chief to create food, but he is busy directing the moving of the statue. I don't think he needs to direct the fishing, since the villagers are successfully catching fish and returning to the ocean for more. The issue is that even with this activity, the supply dwindles.
When I quit the game and came back to it, as Barbara requested, the food supply was about 5300, but of course, everyone had stopped working on the statue. The food supply is decreasing once again, even though they continue to fish.
I guess the strategy is to shut down the game in order to amass a substantial amount of food (although this means losing progress on the statue puzzle), then log on again and resume pushing the statue up the hill until food runs low again, quit for a while and start the statue work again.