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It means Under no condition, never, and noway nohow.

"He says he'll pay me back on Monday."
"In a pig's eye he will!"

When I hear it I tend to think of the American South, although it's used all over America. This is one of those idioms that work best with a slight western drawl.It been around since at least 1872 when Petroleum V. Nasby (AKA David Ross Locke) used it in a newspaper column. No one knows exactly what it means -- perhaps that the idea would seem ridiculous even to a pig ('in a pig's view'), or perhaps comparing the wisdom of the stated idea to the wisdom of sticking something in a pig's eye. Or something completely different.

Somewhat akin to when pigs fly.