I actually need to applaud the Pathfinder writing crew for, so far, doing an excellent job on explaining how to pronounce most things in the world. Rise of the Runelords has been particularly great in this regard. I'm also thrilled at how much of this has transferred over to the community wiki. That said, I haven't been able to find a good answer on Cheliax.
Some options my group has thrown out:
The intuitive "Chel-ee-axe,"
The exotic "Shel-ee-uh,"
And something that sounds like shellac from one particularly tired player. Also, the ubiquitous chillaxin' joke has made an appearance.
So, gentlemen, what's the proper way to pronounce Cheliax?