The (apparent) fact that the US civilisation is heading towards a major change is what it means to be chaotic. Civilisations progress towards order, but if they don't collapse due to outside events, they collapse under their own weight (or more often, it is a combination of events that the civilisation cannot handle). Such events are often unpredictable, and seemingly small things can have large ramifications - that is key to the (mathematical) definition of chaos.
Anyway, my point was that it does not make sense to make predictions such as "in a thousand years, our civilisation will be able to seed the galaxy with DNA" or "a civilisation a million years more advanced than us could do such-and-such". Whether you call civilisation a chaotic system, or an ordered system that often collapses, makes little difference to the unpredictability of it over such a timescale.