Automated poultry processing lines still rely on humans to lift slippery, easily bruised carcasses onto a shackle conveyor. Deformability, anatomical variance, and strict hygiene rules make conventional suction and scripted motions unreliable. We present ChicGrasp, an end--to--end hardware--software co-design for this task. An independently actuated dual-jaw pneumatic gripper clamps both chicken legs, while a conditional diffusion-policy controller, trained from only 50 multi--view teleoperation demonstrations (RGB + proprioception), plans 5 DoF end--effector motion, which includes jaw commands in one shot. On individually presented raw broiler carcasses, our system achieves a 40.6\% grasp--and--lift success rate and completes the pick to shackle cycle in 38 s, whereas state--of--the--art implicit behaviour cloning (IBC) and LSTM-GMM baselines fail entirely. All CAD, code, and datasets will be open-source. ChicGrasp shows that imitation learning can bridge the gap between rigid hardware and variable bio--products, offering a reproducible benchmark and a public dataset for researchers in agricultural engineering and robot learning.