What Is The Origin Of The Phrase 'I Would Give My Eye Teeth For That'?

"To give one's eyeteeth for" has been a popular figure of speech meaning "to be willing to undergo great sacrifice for" since at least 1930, when it was used by Somerset Maugham in his comic novel "Cakes and Ale." One's "eyeteeth" are, as you say, the upper canine teeth, so called since about 1580 because they are directly under and closest to the eyes. Not only are eyeteeth functionally valuable, being used to bite off and chew food, but any damage to them is likely to be very painful, as the nerves of these particular teeth run close to the eyes and the pain may actually be felt in the eyes. So to voluntarily suffer loss of one's eyeteeth would indeed be a great sacrifice, perhaps not as profound as "giving one's right arm for" something, but still a major drag. It would definitely make eating pizza (my personal quality-of-life standard) difficult, for instance. An even greater sort of sacrifice, however, would be "to give one's eyes for," a hyperbolic metaphor for sacrifice that dates back to 1857.