For a BR song, this one has a pretty accessible meaning. The "chaos from within", simply put, is fear of external threats and our propensity towards emotional overreactions. Humans have evolved innate tendencies towards tribalism, and Greg is suggesting that we should be weary of our tendency to let terror rule us. Nothing to fear but fear itself? We need to act more on reason and be less motivated by primordial fears. This can obviously apply to Trump's stoking of racial tensions, immigration fear-mongering, and other forms of US tribalism, but the song's meaning is even more universal than domestic politics.

I also love the line about the predator wallowing in failure in the face of consciousness. It's saying our sentience allows us to conquer nature and rule over the earth, but we're still scared of the outside world more than we should be, and instead we should be more focused on avoiding the mental and emotional pitfalls of that sentience.

The one phrase I've never heard before is "the fox-stained leaves of civilization". It sounds like a phrase Greg borrowed from a philosophy book or something, but I couldn't find anything online. I'm assuming it means the bloody pages of history, but a fox is really more of a brown/gold color. And what happens to really old paper pages of a book, they get brown with age. So maybe he's just saying the ancient pages of the history books, instead of blood? I think the blood metaphor fits the theme of the song better though. I'd like to hear others' interpretations. :D