Anything you will build will almost certainly be illegal and you could land up with a heavy fine or time in prison. It would be incredibly difficult to build a killing trap that would meet current legislation and it would cost a lot of money.
You could hire someone with a suitable gun licence to come a deal with the fox, but if you're protecting your chickens so badly you will probably be visited by more than one fox over time, and as you know it only takes one visit.
i'd agree with Jules77, spend the time and money building better protection for your chickens then it doesn't matter how many times they come visiting.
I also suggest you contact the 'Fox Project' in Tonbridge, Kent who have excellent advice on fox deterrence and although being pro-fox, take a very matter-of-fact view about such issues.