That's right George. But dead foxes will eat no chickens. Nor will they produce any baby foxes.
Steel leg traps like this will work fine.
http://www.rpoutdoors.com/viccoilsprin.html
Victor 1.75 4 Coiled Coilspring
5 3/8 jawspread for fox, badger, bobcat, lynx, nutria, coon, coyote and Possum.
0478
$16.00, 6/$89.00, 12/$169.99
This same company also sells snares. I REALLY like these.
http://www.rpoutdoors.com/qk66snares.html
$1.79 a snare!
Made with 1/16 inch cable. It is plenty stout enough to catch any fox out there. Again, watch some YouTube videos on "How to snare foxes and coyotes". These professional trappers will give you the very best ideas on how to place and, set snares. The same techniques work equally well on both foxes and coyotes but, you can use smaller wire for foxes. You can set dozens of them very inexpensively. If you are the least bit handy with tools, you can buy the snare components and make your own. I catch coyotes by setting my snares where they are crawling under a fence or squeezing between objects. You can even create a sort of funnel by strategically placing twigs to guide them right into your snare.
A game cam will give you perfect information on the times the fox is visiting. A well-placed shot from a .22 will solve your fox problem. Walmart sells pellet rifles for a little over $100 dollars that work very well at shorter distances. Pellet rifles are much quieter. Just be sure to buy the ones that shoot over 1000 feet-per-second. You have a choice of pellet size. I like .22 caliber pellets. A little slower but has the mass to punch into the vitals.