give (one's) eyeteeth

To go to any length or relinquish anything of value in order to have or be able to do something. Almost always used after the modal verb "would." Oh, I would give my eyeteeth to be able to write like you! You mother has always said she would give her eyeteeth for your beautiful curly hair. I love to bake, so I would give my eyeteeth to have a huge kitchen like this!

give (one's) eyeteeth for (something)

To go to any length or relinquish anything of value in order to obtain some specific thing in return. Almost always used after the modal verb "would." Oh, I would give my eyeteeth for curly hair like yours. She said she'd give her eyeteeth for a chance to meet the singer in person. I love to bake, so I would give my eyeteeth for a huge kitchen like this!

give one's eyeteeth

Also, give one's right arm. Go to any lengths to obtain, as in She'd give her eyeteeth for a mink coat, or He'd give his right arm for a new car. These hyperbolic expressions both allude to something precious, the eyeteeth (or canines) being useful for both biting and chewing and the right arm a virtual necessity for the 90 percent of the population who are right-handed. Both date from the first half of the 1900s, when the first replaced give one's eyes, from the mid-1800s.