Is it possible to shove a whole chicken down my snake?

  A chicken I can buy at the grocery store. Will it painful for my snake?
No not if the snake is big enough. A food item should leave a slight bump within a snakes stomach after consumption. Any bigger bump then it may struggle with it
I fed an adult Python chickens that were raised for FFA show. I guess you can only show one chicken in the show and the company gave each kid like 20 chics to raise. I put the chickens down in a humane way, froze them, and then fed them to my snake.
If you "shove it down," yes, it will be painful and could cause damage, especially of your snake is a smaller species. Best to feed it on defrosted rodents and leave it at that.