In English we pronounce "choir" to rhyme with "inquire", but there is neither a "w" in "choir" nor a "qu".
The answer is that English spelling never keeps up with English pronunciation. See "Two, too, and to are pronounced the same, right?" and "How do you pronounce two, too, and to?" And sometimes the spelling changes even if the pronunciation stays the same.
"Choir" was once spelled "quer" and an archaic form is "quire". The "quer" (kwer) was from the then French word for "chorus".
You might think that the spelling and pronunciation of "choir" was also French, but "choir" (kwahr) is a variant of "fall". The French use "chorale". Apparently "choir" was somebody's idea of making English spelling conform more to Latin or French. See "Linguists: why is 'choir' pronounced 'quire'?" for an amusing discussion. For a more serious discussion of English spelling see "Why not Spelling Reform?" It is a bit long and I have yet to finish it.
