I would link ethics to consciousness, through intersubjectivity, with the mirror neurons needed for learning by copying, leading to empathy, & principles like The Golden Rule, and the Categorical Imperative, and also underpinning the extended human capacities for communication. Discussed here: Is the Categorical Imperative Simply Bad Math? :) But, morality is intrinsically a social phenomena, so I'd look to Durkheim's sociological view of religion, for understanding how contention between moral systems has been about the binding power of enacting 'shared attitudes to sacred things', eg habeus corpus & jury trials, as much as altars. See Haidt's Moral Foundations Theory for how agrarian vs pastoral societies seem to have different moral values.
Chomsky believes in an 'innate moral grammar', by analogy with his views on language. See 'Is there a Sense of Justice? Comments to Noam Chomsky on Innate Human Morality'. I'd say it faces a similar problem, of being barely falsifiable. It ends up being that whatever biology is found, it is called innate. But biology & evolution are profoundly versatile & flexible, as are minds & culture.
Consider the puzzle of the almost complete uniqueness of humans, in their having sex overwhelmingly in private, discussed here: How do ethicists tackle the question "Is it immoral to have sex in public places?" Is it possible to use rational and empirical ideas to answer? Is it innate biology? The rarity implies it isn't. I'd say game theory, & the 'reprogrammability' of social dynamics by hijacking shame & disgust into cultural structures explains it (it helps us cooperate better, but it hasn't been a rational or even conscious choice). But then it can be asked, is that hijacking of evolved responses by culture, biology? You can shift the goalposts & say it's 'innate culture-making' or whatever.
The Dunbar number shows our neocortex evolved for navigating social landscapes & impulse inhibition, so really culture & biology have converged. And I'd suggest psychopathy, and other conditions, imply that different or less consistent pressures could result in very different outcomes over short evolutionary time-scales. The persistence of a low percentage of psychopaths across every culture, is more readily understood through game theory, than purely as a pathology or developmental failure. Anyway, you didn't ask for a critique.
Probably what Chomsky has in mind is work of people like Yale psychologist Paul Bloom, eg 'The Moral Life Of Babies'. See a good summary of the history of the issue & current science here: Is Humanity's "Moral Sense" Inherited or Nurtured?.
For me, it's like the nature/nurture debate about humans in general: largely an obscuration rather than a help, to good discussion & science.