How awful! Chicks are vulnerable, because they are small, and this cat is a serious predator, and your birds didn't have a tough broody hen to defend them.
Definitely reinforce your coop and run! Most of use have learned the hard way that building 'Ft. Knox' is best, and it all gets improved after every disaster.
I would talk to the neighbor, if you can. This may go well, or not.
Photos help, although it's too late now for this episode.
The only good news here is that only one bird was killed, not everyone. A weasel could have entered the same way, and killed everyone in a short time. Now this access point will be fixed before worse happens.
If one of my animals causes harm, I would pay for it. that's the responsible (and legal) thing to do. It wouldn't replace your loved cockerel, but still would help.
Electric poultry netting, or electric fencing with wires close together would repel this cat, and other land predators.
There's the 'trap and shoot' method, or trap and take to Animal Control.
Mary
