Cats and ocelots are completely different animals now days.
And I don't think tamed cats/ocelots ever killed chickens.
According to the Wiki, untamed ocelots kill chickens and baby turtles but that hasn't been updated, it still says tamed ocelots turn into cats which is no longer true. I don't know whether ocelots can still be tamed, if so they stay ocelots and probably won't kill chickens, though I'm not certain.
Untamed cats are supposed to kill rabbits (I can verify that) and baby turtles.
According to the Wiki foxes can be semi-tamed, turned "trusting", there is no mention of that stopping them from killing chickens.
Or just wait for it to go in to kill the chickens and close the doors, maybe iron doors closed by redstone so you don't get close enough to scare it.
Or maybe better have a drop with open trapdoors to trap it automatically, the Wiki claims they are immune to fall damage so you wouldn't have to worry about that. You'd still have to be around to nametag it to stop it despawning but you wouldn't have to get close until it had been trapped.
For my mini-feather/egg/raw chicken farm I use only chickens, double chest, a droppervator, lever, and a dispenser. (With hoppers for collection and transport, of course) No additional mob type is needed.
When done correctly this will eject eggs automatically from the dispenser, causing baby chickens to hatch, automatically. Semi-manual intervention is needed to easily collect the various drops. (The lever)
I've attached some screenshots of my setup. Note that it uses some redstone+comparator setups. If you're comfortable with redstone this shouldn't be a terribly tough build.
Notes on the screenshots:
1. It's a 4x1 area for the chickens. This causes them to exceed the allowable space and die as babies mature.
2. The red granite trio of blocks is optional. It's an AND-gate hooked up to a redstone clock pulsing every few ticks (any kind will do). This helps minimize the risk of the droppervator getting "stuck." Specifically I used a container with one item+comparator/repeater clock (not shown).
3. You'll notice that I have two levers to control the flow of things. The "autobreed/collect" lever is the only one that's "required" as if this is omitted you'll struggle to effectively collect non-egg items. The DC shown is the destination for the droppervator items. It's where everything will end up if you put it into collect mode. NOTE: Collection takes time. Be patient.
4. The secondary flow lever is left over from some experimentation. I found it occasionally useful for some fringe scenarios.
5. The non-collection chests are so that you can leave the main flow regulator in COLLECT mode and periodically, manually, transfer eggs to those chests. This allows for semi-automated operations while minimizing losses of feathers and raw chicken.
Note on the build:
1. It's NOISY. Between the incessant clucking of the chickens and the click-click-click of the dropervator I wish I had put this in an out of the way place on this map. I find it unpleasant to be around. But, it is a "Mini" build, so I couldn't make the droppervator silent.
2. There is no integrated item sorter. The space and materials requirements I was working with on this survival map (i.e. very early game) prevented me from putting an item sorter into the mix. On prior maps I've integrated these with great success. The chicken and eggs breed non-stop making the only reason to switch to collection mode my want to retrieve eggs.