I just flew this same easter island trip on LAN from SCL two weeks ago!

The check-in desk closes 1hr prior to departure, no exceptions are made as this is treated as an international departure, so the manifest is uploaded for security reasons and closed at that time. If you can get a real boarding pass ahead of time (maybe from your origin airport??), do so! The ones I got from online checkin had a watermark saying must see agent to verify passport). *You board from a domestic gate so be sure to go through the domestic security checkpoint*. this meant we could not experience LAN's brand new airport lounge

My flight was delayed 6 hours due to "ATC Congestion". The flight the day before had flown 3 hours then turned back due to weather on the island, so they took our departure time of 10:15 and we left at 3pm. ATC for easter island requires three HOURS of separation between aircraft since there are no diversion points along the way. I read up about this and talked to the pilots--ATC is so tightly controlled there that no other airline/aircraft is even allowed to name Easter Island as an alternate/diversion point during the time that a LAN aircraft is past the "Point of no return" a bit halfway through the flight until the time it clears the runway.

Easter island was a blast, though we only had from 10pm till 4pm the next day. I chickened out on coming without a hotel reservation in hand, so I booked the Taha Tai hotel as we were boarding. Taha Tai proved to be an excellent choice (the entire LAN crew went there too). I had trouble calling the hotel even with my worldwide tmobile phone. My wife and I just started laughing when I gave in and got a cab, and the driver said the fare would be equivalent to $2.00 USD.

If you rent a vehicle be aware that as of 2 weeks ago there are security stations/roadblocks leading both directions (towards the statues and the beach). They will not allow you to pass without an local/island tour guide. They had a fatal tourist accident recently and they were doing this to prevent any reoccurrence. A second checkpoint eventually relented when they saw my son, took down all info from the car, had us sign saying we would just go as far as the beach and turn back around within 2 hours.

When we went to return the rental car, the employee in town told us to park it at the airport. Anywhere. Unlocked, and set the keys on the dashboard.