To nucleate a crystal of ice from water requires an activation energy, so if you cool perfectly pure water to 0°C it will remain liquid indefinitely. You would need to cool it well below 0°C to make it freeze (I think this happens around -50 to -60°C).
In practice water contains impurities. These may be dust particles, bacteria or even just small bubbles of dissolved gas, and these impurities reduce the activation energy required to nucleate an ice crystal. The result is that ice crystals nucleate at impurities at temperatures well above the -50 to -60°C mentioned above, which is why I can make ice cubes in my fridge freezer even though it's only about -10°C.
If you reduce the water temperature to just below zero, e.g. -1°C, then only a few of the impurities will affect the activation energy enough to nucleate an ice crystal. The result is that only a few crystals start growing, and once the water has frozen you'll have a few large crystals. If you rapidly reduce the water temperature to well below 0°C then many more of the impurities will be able to nucleate ice crystals and you'll end up with many small crystals. So in general slow cooling rates give a few large crystals and fast cooling rates give lots of small crystals.
However you are talking about a chicken not water, and this raises a complication because the water in chicken contains dissolved salts, sugers, proteins etc from the flesh of the chicken, and consequently it's freezing point is lowered to below 0°C. Another complication is that as the water in chicken freezes, the solutes are excluded from the ice crystals and the concentration in the remain water increases, which lowers the freezing point even further. So the water in chicken won't have a single freezing point. Some ice crystals will form a bit below zero but to freeze all the water needs a significantly lower temperature. So your chicken at -3°C almost certainly contains a mixture of ice crystals and unfrozen water. This means you can get Ostwald ripening, which causes small crystals to shrink and large crystals to grow.
Incidentally, while Googling for information on the freezing point of chicken I found this article that you might find interesting as it covers the points I've made in a lot more detail.