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8.
To snap the neck of a chicken, usually immediately prior to butchering.
"Wilber, fetch me a chicken for dinner."

"Alright, ma! Just hold on, I need to choke me a chicken first!"

"Cluck, cluck, cluck, CLUUUUUUUUUCK!!!!"
by General Cluck-Cluck June 13, 2003
 
9.
to beat your wife and eat your meat
eatin an beatin
by sir dan May 12, 2003
 
10.
well there was this chicken named mike who lived a normal chicken life untill he had his head cut off. Despite the decapitation mike was able to lead a pretty normal life for 18 months untill he finally choked to death.

Although tragic i think it may explain the saying.

Maybe not.
Choking+Chicken=choking the chicken
by arzoo October 18, 2006