A different option so seemed worthwhile putting as a separate answer:
http://www.kayak.co.uk/#flights/ANC-ADK/2012-05-17-flexible/2012-05-22-flexible
If you can get to Anchorage, it’s .. well… also horrendously expensive, but if you can get a cheap way to Anchorage, it may save some.
Again, Sunday and Thursdays seem to be the only days flights are active on.
After a little searching, there are still flights on a couple of days, if you’re prepared to go to Vancouver first. It’s not cheap, however:
http://www.kayak.co.uk/#flights/YVR-ADK/2012-05-17-flexible/2012-05-22-flexible
Much like the other reference, it appears to only have flights on Thursdays and Sundays. Still, that’s better than the once a week flight to and from Tonga I took from New Zealand 😉
EDIT:
Hey look at that, for a similar rate, you CAN get your flight from Chicago:
http://www.kayak.co.uk/#flights/CHI-ADK/2012-05-17-flexible/2012-05-22-flexible
Credit:stackoverflow.com‘
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