Shooting a hawk is not worth the fine that comes with messing with a migratory raptor. By negative re-inforcement I meant shouting it off, or maybe shoot of a whistling bottle rocket. Whistles have a pretty good effect on most animals and scaring the bejesus out of them. However, since trapping season varies state-by-state for falconers, and you're saying it's not afraid of you, it sounds like it's a juvenile hawk that some falconer would be willing to come out and trap for you, and take them as their own hunting bird.
I would go here: http://tennesseefalconersassociation.com/Tennessee_Falconers_Association/Welcome.html
Click on the link to Contact TFA, and say you have a hawk killing your chickens, and you were wondering if there were any falconers willing to come out and trap it. Try to be specific and let them know whether or not it was an adult. If it was an adult Red-tail it would have a red tail, if it was a juvenile it's tail would be brown.
Better to play it safe, than sorry.
Thank you for info!! I will contact them.... Just 1 more question.... If the hawk flew away and we haven't seen it since, how do you trap it?