To yearn for; to go to any lengths to obtain. The eyeteeth, the upper canines, have been so called since the sixteenth century, presumably because their nerves are quite close to the eyes and a toothache in those teeth is felt as pain in that area. Since they are extremely useful for biting and chewing, giving up one’s eyeteeth entails a considerable sacrifice. However, this hyperbole most likely began life as to give one’s eyes, a greater sacrifice still. Anthony Trollope used it in Barchester Towers (1857): “Bertie would give his eyes to go with you.” Substituting eyeteeth, it is a safe guess, simply made the expression more colorful rather than affecting the underlying meaning in any way. It appeared in W. Somerset Maugham’s Cakes and Ale (1930): “He’d give his eyeteeth to have written a book half as good.” See also cut one's teeth on; give one's right arm.