According to Google, it used to be spelled exactly like it's pronounced (ie. "quire"), but it's spelling was changed to more closely resemble the French "choeur".

It's hard to answer without speaking it, but it sounds like "quire" or "k wire" or "kw eye or"

Thanks to Jmat, I found the thread: Why is 'choir' pronounced kwʌɪə? [quire] http://forum.wordreference.com/showthread.php?t=2117387&langid=18 Wordreference forum member 'ewie' wrote: " The question you should really be asking, Karen, is: Why is the word kwʌɪə spelt 'choir'? It was originally spelt quire, and borrowed from Old French quer. Some time in the 17th century people started spelling it choir so that it would look more like Modern(ish) French choeur. The new spelling remained ... alongside the old/original pronunciation"