Chests are pretty random. Sometimes there will be plenty of them. Sometimes you go around just trying not to starve.
But... I don't know, I always was attempting non-Slut runs, — meaning I did no farming, and I only starved once in the beginning. Food doesn't seem to be a problem. I have good Agility and Perception, I eat Harpy eggs, I find chests, sometimes buy meat from merchants, and it feeds me until I meet the Demon King which rewards you with 200 of Food if you defeat her.