The chicken squeaks on both out-breaths (squeeze) and in-breaths (release). The timbre is distinctly different between the outs and the ins. Additionally, if you listen to the bridge around :46 the squeaking is outside of the comfortable range of the toy and the tone is yet more distorted. So if they did use a sampler, there was serious attention to detail: it would need to be performed on two different keyboards using a set of samples for different pitch ranges.
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