A colleague is trying to find this, and we're struggling, seeing only connecting flights via Lima or Panama. Are we missing something? It seems odd that two South American capitals aren't directly connected...
You can actually easily check where you can fly from Quito via the Airport's Website looks like you are able to fly to Guayaquil
It's been more than one year since the original question, so I guess these flights were not available back then, but now LAN Chile offers direct flights from Santiago to Quito, but not the other way around. I checked the schedule on momondo for a few days in March 2015, here is an example.
One-way flights for those days cost around 647 euro, but it reduces to around 500 euro if you book a return flight, so even if you're not planning to take the flight back to Chile, it might make sense to book it that way. I haven't checked it separately, but sometimes you get a better deal if you book open-jaw tickets rather than buying a one-way ticket, e.g. Santiago-Quito-Lima may be cheaper than Santiago-Quito for certain dates.