Chickens have nothing to do with chicken pox.
It was so named to distinguish the weaker form of the highly contagious but usually nonfatal pox from the dreaded and extremely deadly form of smallpox.
Because smallpox was named first, doctors needed a timid name for its less lethal cousin.
To make it clear, they chose the unscientific but unassuming chicken.
Chickenpox was first identified by Persian scientist Muhammad ibn Zakariya ar-Razi (865–925).
It was known to the West as “Rhazes”, who clearly distinguished it from similar diseases such as smallpox and measles.
Giovanni Filippo (1510–1580) of Palermo later provided a more detailed description of chickenpox, which is also known as varicella.