> Altruism in large social groups is something chimps haven't worked out yet

But their close relatives, the Bonobos, apparently have.

From https://en.wikipedia.org/wiki/Bonobo#Behavior:

> Primatologist Frans de Waal states bonobos are capable of altruism, compassion, empathy, kindness, patience, and sensitivity, and described "bonobo society" as a "gynecocracy".