The Minhag of Kaporos dates back at least 1500 years, and is mentioned by the Gaonim in their Responsa as symbolically replacing a Korban to atone for our sins. Additionally, the Ari zal was a strong proponent of this custom for Kabbalistic reasons. Nevertheless, it was not without controversy, and the Ramban and Rashba forbade it.
The Gaonim discuss the rationale for specifically using a chicken, and one reason given it that the Aramaic word for chicken "Gever" is similar to the word "man", strengthening the parallel that one should associate himself with the slaughtered fowl and picture himself deserving of such a fate. Hopefully, this is a powerful tool to motivate one to Teshuva.