People used to call Cooper's Hawk "Chicken Hawk."
They are not rare across the entire US, but can be difficult to distinquish from their Sharp-Shinned Hawk relatives. Often impossible, so people like me just call them "Accipter sp.". In the US, there are 3 accipter species, all bird-hunters. The noble Goshawk, beloved of falconers, is the king. Rarely seen.