Paul, I was quite amused to see the two-star rating for my earlier answer. Read on to find out why. Most British reference libraries keep a copy of The Oxford English Dictionary. It consists of 20 volumes, looking for all the world like a set of encyclop�dias. It is regarded by etymologists and philologists - language experts - as the grand-daddy of all dictionaries...the 'bible' of English word and phrase meanings/origins. Next time you're in a library, pick up the volume with "chance" in it. The first main entry deals with all the different aspects of "chance" used as a noun. Pass over these to the next main entry, involving "chance" as a verb. There are five numbered sections and sub-sections. Check out No. 4c. You'll find out that it says exactly what my earlier answer claimed about the origin of "chance your arm". That's where I got the answer from. It's not every day that a 'bible' gets two-starred! Cheers.