Greetings from a BYC site lover and professional wildlife biologist. No, a bobcat will NOT attack a small child (unless you are in the habit of leaving your newborn unattended in the woods overnight). They are very small cats and prey on small game. They are not even remotely dangerous. Bobcats look much bigger than they are but it's all fluff. A full grown bobcat seldom weighs more than 20 POUNDS. So they are approximately twice the size of the average 10 pound house cat. (I have a house cat that weighs 18 pounds and I certainly don't see anyone running in terror from him). Bobcats feed primarily on rabbits and rodents. They can certainly kill a chicken. They will also prey on young deer fawns. However, they do not attack humans and on the occasion they do take down larger game it's because the animal was sick/injured/dying.
I've had more encounters with bobcats in the wild than I can count. These are not dangerous animals unless you are a rat or mouse. I've approached a female with kittens in broad daylight within 10 feet. I've observed half grown deer interacting with a bobcat. The deer weren't even mildly alarmed, not even bothering to move or cease browsing even when the bobcat was within pouncing distance.
The taking of one chicken, although heart breaking, does not constitute a nuisance bobcat. Bobcats are primarily active in late afternoon/evening and early morning. You might try getting your birds housed in the coop earlier in the evenings, especially at this time of year, to deter further depredation. Repellents should work well and are easy and inexpensive, human urine being the cheapest and easiest of all! Bobcats have very large ranges and the amount of time it spends near your particular property will be limited. It's also possible that this was a young cat in the process of dispersing and may have already moved on as it seeks an available territory. In that vein, removing one only leads to a vacant territory that will attract another.
Bobcats have faced increasing pressure for small game as coyotes have expanded into areas where they did not historically occur (the eastern United States). In some states, such as Iowa, bobcats are listed as state endangered/threatened species. In all other states they are listed as a fur bearer. If you intend to "take" the animal then you will need the appropriate permit within season unless you can obtain an exception from state game. In some states bobcat hunting/trapping tags are limited and based on a lottery. And one must purchase that tag. Otherwise you are in clear violation of the law and all associated penalties apply. The taking of a wildlife resource that belongs to The People is an act of theft clear and simple. It is a way of saying to your neighbors and community, hundreds of thousands of people, that you and your interests are more important and that you are above the law.