I have been hearing many people say that it is best for humans to eat every 3-4 hours while awake.
Does scientific evidence support this claim?
It depends for which aspect of human health it should be "best". From nutritional perspective see this quote from When to eat and how often? in American Journal for Clinical Nutrition:
The effect of the timing of food intake on metabolism has been the subject of active investigation for >40 y. Indeed, whether it is “better” to eat many small meals a day is one of the questions most frequently posed by the lay public. Comparing the potential benefits of nibbling and of gorging has been the focus of much animal and human research, but no clear consensus has emerged (1-7). Simply put, the question of whether there is a health benefit from the consumption of multiple small meals will ultimately depend on how much energy is consumed, as opposed to how often or how regularly one eats.
Many interesting things about body weight, body composition, blood markers or metabolism can be found in that article from International Society of Sports Nutrition but its overall conclusion seems to be that:
(...) research to date examining the physiological effects of meal frequency in humans is somewhat limited. (...) Until more research is available in the physically active and athletic populations, definitive conclusions cannot be made.
But you may ask about another aspects of human health: tooth decay, insulin secretion, glucose level etc. Unfortunately, it seems that for every of this aspects you have to search scientific databases independently. This is complex matter and there may not be general answer. Also, there may be strengths and weaknesses to many different meal frequencies wihout any ideally good one.