I can run Chrome X86 on a few machines here and have a few WiFi dongles but you left out all details so I can't check to see if I have a similar setup.
So my advice is to keep trying dongles.
I have converted an old Gateway laptop to a chromebook. All works well except the wifi. It was working when it was running Microsoft Vista. I converted it and it works fine if I plug into the internet, but no wifi is even detected.
I tried a new wifi USB plug in device but the wifi is still not recognized.
Any thoughts?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic