well i am a little fuzzy on all the details but in my understanding, in california there are provisions for people to run animals on national forest
land and even on other peoples properties if they border national forest land (like just about everything out here in the north does).
so people who have goats, cows, etc can roam around the forest grazing them, and even onto other peoples properties. the latter probably only happening accidentally, but if i am correct here, it is technically allowed. i would assume this also means it is ok for you to have chickens there.