Middle English foode, fode, from Old English foda "food, nourishment; fuel," also figurative, from Proto-Germanic *fodon (source also of Swedish föda, Danish föde, Gothic fodeins), from Germanic *fod- "food," from PIE *pat-, extended form of root *pa- "to feed."
Food chain is by 1915. Food poisoning attested by 1864; food processor in the kitchen appliance sense from 1973; food stamp (n.) is from 1962.