Sounds like a Cooper's hawk...google it and see it that's what you have. We have them and redshoulder hawks. Glad it didn't get your chicken.My poor babies are terrified now. 3/4 of them ran back to their pen, which is roofed and covered by wire, and most of the rest won't leave my front porch even to chase bugs. The 2 geese and 1 chicken are glued to my hip.
I have no clue what type of hawk it was, it was small, and was a grey color with black stripes on its feather. I'd almost think falcon but we don't have those in Texas do we?
Don't know how many falcons but there are peregrine falcons up in the north texas area.