give your eye teeth for
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.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
give your eye teeth forgo to any lengths in order to obtain something.
The eye teeth are the two canine teeth in the upper jaw.
1930 W. Somerset Maugham Cakes & Ale He'd give his eye-teeth to have written a book half as good.
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