Blue Chicken Egg

It is a Traveling Merchant line, so you cannot plan around it. He carries it at random, the price is steep for something with no combat value, and there is no other source, which means you take it the day it appears or wait an unknown number of days for the next chance.

As a pet it behaves like the rest of them. It follows you, nothing can hurt it, and it does nothing beyond existing. The only real decision is whether it is worth the pet slot over one of the pets that carries a light source.

The chicken is lifted straight out of Stardew Valley, where a blue one is a rare variant you unlock by befriending a particular townsperson, which is the joke in the buff text. The reference does not survive the trip cleanly: over there the blue birds hatch from ordinary white eggs, and a blue egg is not an item that exists.