Altitude sickness

Since I will soon be going to Chile I am reading bits and pieces about it. There seems to be quite a bit mentioned about altitude sickness.
I wonder?!?!? I haven't decided whether this is something I should be worrying about. But on the plus side I guess that in Chile you are never really far from the low elevations so it is not a huge concerned.
But I just found more information that you could possibly want on altitude sickness on the website for the Beijing-Lhasa train.... This sounds like a fantastic trip and the one way ticket is less than US$200 !!! (OK; I'll admit I was NOT looking for altitude sickness information at that point)

Have a look at this dream train trip: here is the link


Added later: you guys cannot be trusted  ;-) I first posted this with "Altitude thickness" as a title (typical English as a foreign language thing) and nobody said a thing!!!!