Re-homing by private citizens is not likely to be legal. Even if re-homing option pursued, fox would need to be moved a long distance owing homing abilties. In all likelihood your fox has a territory, possibly in cooperation with a mate, that is patrolled consistently with routes for hunting and territory maintenance. You may catch and release as a repelling measure but odds are you will simply be making fox trapwise. Dispatching fox can provide short-term security since replacement may not adopt same routes, at least until your flock is designated easy eats. With some types of chicken and locations where they are free-ranged, the birds can be hard for fox to catch if birds fly up into trees or buildings. Most chicken no longer suitable for that. You can make so fox has no way to get at birds (coop / run) or use dogs to repell. I use all three methods and fox still probes although dog has caught one and nearly another. Close call with dogs makes so fox does not visit for a couple weeks or more before probing resumes.