Adult chicken get damage when you push them on a solid block.
Also when they run at a wall.
Seems like there is a wrong Hitbox (maybe the hitbox of a young chicken) for checking the movement of a adult chicken, or an default Hitbox of (Zombies/Players ore something else) is used for the suffocating-damage-Check
Related issues
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Duplicate Bug: https://mojang.atlassian.net/browse/MC-9540
This ticket has been marked as a duplicate of MC-9540, in favor of the better description/information provided.
After a restart of the Server the adult chicken don't die.
Looks like only growed up chicken are affected.