I was always really careful about using essential oils in the house when we had our dog. Although I have some books which have recipes for pet pest problems that have recipes including essential oils I just stuck to plain water as much as possible.
Couldn't resist sending a piccy of the old fella, who would be loving the snow if he was still with us.

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His sense of smell was much more sensitive & that concerned me with EOs and also didn't want to risk him licking it and ingesting any. There are stories on the net about small animals dying from tea tree oil exposure but I have no idea if these are true or just hype
You use pretty low concentrations of EO on humans for massage (half the number of drops to the number of mililitres carrier oil), so at the very least I would think you'd need to take that down by a ratio to take account of the smaller body size and so smaller internal organs to deal with toxicity.
I have a book suggesting infusing olive oil with calendula, as a gentle anti-bacterial & antiseptic for irritated areas.
Maybe I am overcautious and know nothing about chickens, so hopefully someone more knowledgeable can help
