I am jot so sure "chicken groove" is the right description for a relief groove. Here is a pic of a muzzle, ready to thread, of a customer who has very specific specs. The relief groove is needed to make sure what ever muzzle device is used will thread to the shoulder. Many muzzle devices don't have much internal thread relief.
Notice how close the tool is to the shoulder. I had to use that angle to be able to see any space at all. Straight overhead there is less clearance.
Not sure why the part looks so scratched up in the pic. To the naked eye it was smooth and shiny.
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Here is it after threading to Class 3A specs.
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