How long does it take to change states of matter?
Part of the answer is that the rate of freezing depends on the heat of fusion of the material being frozen (relatively large for water, the chief ingredient of uncooked chicken), but smaller for other substances). 

Another piece of the answer is that an object can lose heat by convection, conduction, and/or radiation. You would increase the rate of heat loss by: 

(1) increasing the surface area of the chicken as much as possible (flattening it), 

(2) placing it against a surface held as cold as possible and made of a material such as metal with high heat capacity; 

(3) hitting it with a continuous blast of extremely cold air or gas at the highest possible wind speed (remember wind chill factor?) and maximizing radiant heat loss by previously having painted the chicken with flat, black paint and conducting the experiment in a mirrored, insulated chamber. Some unusual materials can be induced to cool by irradiation with a laser (this is how we have obtained the lowest recorded temperatures ever) but this will probably not work with chicken. 

I do not think there is an absolute limit on cooling rate, just diminishing returns for increasing energy expenditure. But I may be wrong. I hope you pursue this until you get an answer that satisfies you. That is how new discoveries are made.