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1.
a phrase of hispanic origin used primarily by illegal immigrants and white kids who think that it's funny. Chinga la migra translates to "Fuck the police." Also "Fuck the border patrol."
Diego: What are you doing back in Juarez, Manolo?

Manolo: I got picked up by la migra, ese, the day before payday.

Diego: Man, Chinga la migra. Pinche putos.
by El Ojo May 15, 2006
 
2.
a phrase used among hispanics in areas near to the US Mexico border. "Chinga" has a roughly equivalent definition to "fuck." La Migra is the border patrol. Often used among deportees.
"I got picked up the night before payday. Chinga la migra."
by hacerle la lucha April 24, 2006