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Lethal injection, usually in the context of animal euthanasia.

Comes from the greenish color of many medical syringes and the large volume of barbiturates they use to ensure a quick and certain death.

Sometimes capitalized or put in quotations for emphasis, i.e - "The Big Green Needle"

100+ Google hits. Deny me, bro.
"When I adopted Rover out of the animal shelter he was a week away from getting the big green needle, I'm so glad I found him in time!"

"It's sick how they dragged out Terri Schiavo's life that way. If she had been a dog they would have given her the big green needle years ago."
by Baroque T. Frankenheimer January 20, 2014