In the past 2 million years, the hominid lineage leading to modern humans evolved significantly larger and more sophisticated brains than other primates. We propose that the modern human brain was a product of having first evolved fat babies. Hence, the fattest (infants) became, mentally, the fittest adults. Human babies have brains and body fat each contributing to 11-14% of body weight, a situation which appears to be unique amongst terrestrial animals. Body fat in human babies provides three forms of insurance for brain development that are not available to other land-based species: (1) a large fuel store in the form of fatty acids in triglycerides; (2) the fatty acid precursors to ketone bodies which are key substrates for brain lipid synthesis; and (3) a store of long chain polyunsaturated fatty acids, particularly docosahexaenoic acid, needed for normal brain development. The triple combination of high fuel demands, inability to import cholesterol or saturated fatty acids, and dependence on docosahexaenoic acid puts the mammalian brain in a uniquely difficult situation compared with other organs and makes its expansion in early humans all the more remarkable. We believe that fresh- and salt-water shorelines provided a uniquely rich, abundant and accessible food supply, and the only viable environment for evolving both body fat and larger brains in human infants.