The phrase "an arm & a leg" was started as a joke on the internet. While its origins are sketchy, many believe it actually has its roots in early furniture production, where a three-legged stool cost less than a regular chair and an armchair more than that.                                                                    Louise Graybiel 7-6-2004

The phrase "cost an arm and a leg," meaning to cost a great deal or an exorbitant amount, is simply a hyperbolic figure of speech comparing the cost of something to the grievous loss of two important limbs.  There isn't really any "story" behind the phrase, other than the desire of whoever came up with the metaphor to impress the listener with the outrageous price of something.  Unfortunately, as is often the case, we have no way of knowing exactly who coined the phrase, although it hasn't been around as long as you might think.  Surprisingly, the earliest known use of "cost an arm and a leg" in print dates back only to 1956, in Billie Holiday's autobiography "Lady Sings the Blues," in which she writes "Finally she found someone who sold her some stuff for an arm and a leg."  It is unlikely that Billie Holiday herself coined the phrase, but she may well have popularized it with her book.