give one's right arm, to

give one's right arm (for someone or something)

 and give one's eyeteeth (for someone or something)
Fig. to be willing to give something of great value for someone or something. I'd give my right arm for a nice cool drink. I'd give my eyeteeth to be there.
See also: arm, give, right
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.

give one's right arm, to

To go to any lengths. Also put as cut off one’s right arm for, this term expresses a major sacrifice for all but the left-handed, perhaps even more so than to give one’s eyeteeth. An Americanism from the twentieth century, it presumably was well known by the time Robert G. Dean used it in Layoff (1942): “He’d cut off his right arm for her, as the saying goes.”
See also: give, right
The Dictionary of Clichés by Christine Ammer Copyright © 2013 by Christine Ammer
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