I find it difficult to understand why Harris tried to go down this path. As an atheist myself, I think it's obvious that objective moral values DO NOT exist. If we accept evolution as being the best explanation for how humans came to exist, we must also accept that evolution has been a continuum, rather than a series of distinct steps. And since there are no moral values that apply across all species, it's logical to conclude that human morality is as much a result of evolution as the human anatomy is, and are subject to the same gradual change over time that is characteristic of most evolutionary processes.In the end, morality is a reflection of the evolved empathy of humans, balanced against our instinctive need for social cohesion. We see murder as wrong, not because God says so, but because those of us who were raised in reasonably functional homes (i.e. the majority) would through empathy feel some of the victim's pain, and society also sees murder as corrosive to social cohesion.
The term "objective" morality is not sufficiently precise. It appears more accurate to say that an objective basis for morality exists, rather than saying "objective morality" exists.
That objective basis can be found in evolution itself. Humans are not the fastest or strongest organisms on the planet -- we don't have sharp claws or teeth. One-on-one with larger, stronger predators, humans don't have much of a chance. The key to human survival, as it is with many other organisms, is the ability to work in teams or groups. A structure for social interaction is absolutely necessary for this, and would evolve simultaneously with the organism itself -- through a cause-effect process which would naturally tend to diminish the prominence of behaviors that didn't work, leaving the behaviors that did work to become more prominent in the organism.This behavior filter is a bit messy -- because socially-cooperative behavior is not the only successful survival strategy. Aggressive or somewhat anti-social behavior also provides some reproductive advantage -- not enough to become as prominent as social behavior, but enough to remain a factor in human behavior overall.
Social behavior would naturally include "fuzzy" concepts like "trust" -- and "trust" would unavoidably include concepts like honesty / deception, theft, and even adultery...moral / ethical values that "magically" have found their way into most of the world's religions.
So...there is an objective basis for morality...and it's tied to survival itself...no God required.