I keep chickens in my backyard, and my two year old son enjoys playing with them. Bringing in a chicken to the library for science storytime seemed a natural fit. We have several different breeds of chicken, but the obvious choice for which breed to bring was the Polish breed. They have big fluffy feathers on their heads that makes it difficult for them to see, and thus very easy to catch. They are also relatively laid back chickens. I originally planned to tell my two year old to catch me a chicken, and then bring that particular bird into the library as clearly toddler-friendly, but it was raining so I had to catch one myself. Luckily all of our Polish chickens are friendly.
We read the book Busy, Busy Chickens and then talked about birds in general and chickens specifically, while I used Chicken Patty as an example. She was very patient as I held out her wings so we could see the different kinds of feathers she has, or held her at an awkward angle so they could all see her feet. I had a cloth on my lap and when she inevitably relieved herself on me, that was both a learning experience and hilarious to the preschoolers.
set up a quick craft involving gluing feathers onto a die-cut bird. While the children worked on the craft I took them aside individually to allow them to let Patty sit on their lap. I made it clear that it was a choice, and if they did not want to hold her, that was certainly okay too. Almost everyone did, some of them multiple times. The parents were almost as interested in holding her as well