Most people would say Chimpanzees (98.6%) but it’s actually Bonobos! Their DNA is 99.6% similar to humans.
Phsyiolocialy speaking, their bone structure, stance, muscle formation and facial features are incredibly similar to our earliest living ancestor, the Australopithecus Afarensis (best known as “Lucy”).
Due to both our remarkable genetic and physiological similarities, we can ascertain a lot about how we-at those earliest stages-behaved, moved, ate, communicated, used tools, as well as what our basic needs were and why we evolved. We have learned a great deal all by studying the bonobo.
Bonobos, for instance, exhibit numerous human-like behaviors (generally for the same reasons we initially had to). They walk on their hind legs a great of the time, they “mate” for pleasure (facing each other to promote closeness/eye contact!) They create and maintain extremely strong emotional bonds with their babies, which they raise until around 6 or 7 years old intimately (though males remain close with mothers their entire lives). As infants, mother bonobos play similar games with their offspring (like airplane and peekaboo). They show signs of extreme love for mates and young. Read more here
The only way they are not similar to human beings (or Chimps, for that matter) is that they very rarely act aggressively. All fights are resolved with sex. (I say sex, rather than mating….because again, in this sense they it is solely for pleasure, compassion, and bonding purposes).
Chimps are much more like humans in that they can be violent, sadistic, and cruel. They wage war, kidnap, and rape.
But it’s more than just genes that determine our behavior.
I’ve listed a good link below to a site explaining the divergence of humans from our early ancestors, along with some info on our common ancestors, to help explain how and why this happened.