If You Can Afford It
Buy them now. If you fly on AA for example (and they fly to Santiago daily) and the price goes down, AND you fly other times, like within a year, you can call them and get a "rollover" which is essentially a refund on the fare in the form of a voucher for travel again within a year.
Caveat - it has to be the same class of flight, that said, generally if you buy an advance purchase ticket the "same kind" means that you are still within the advance purchase requirements ( e.g. not a fare that leaves a day later) and is restricted fare. Normally I have found when this has happened, and it has, the fare you are now finding is similar enough to what you bought ahead of time.
You can even do it more than once though it is not often the fares go down that much or that often.
OTOH, I fly to SDQ 5 or 6 times yearly, and my general pattern is to buy one trip ahead, e.g. I have my April 12th ticket now and normally when I get back I'd buy the may ticket. I usually, however use points to upgrade to 1st class so I have my may ticket as well, as lead time is usually adviseable for getting flights with upgrade seats on it.
When I get back from April I would buy my June /July ticket, and when I am back in May my August long weekend trip etc. So I have not failed to flind a flight yet.
However, I am not seeking bottom dollar either so whatever the price is I will pay it or sometimes pay for full fare 1st class if the price for advance booked is very high ,e g. each year at Xmas I don't bother to look, I just treat myself to full fare J class for maybe $600 CDN more than the cheapest coach (normally the difference is $1,800 CDN) . I get more points too when I fly that way. But really it is because the differential is so small I don't care.
If you are flying charter (I have no idea if there are charter fares to Santiago) then you bought it you live with it. But often so cheap who cares?