Hello and thanks for using Just Answer.
I am Al and am happy to assist you with your enquiry.
This restrictive covenant is quite common and was no doubt imposed may years ago.
The law relating to restrictive covenants is complicated, but in simple terms a party who has the benefit of such a covenant can not enforce it unless they have retained an interest in any adjoining land. I am guessing that the person who imposed the covenant no longer owns any of the adjoining land and could not therefore take any action against you for breaching it, if indeed he ever found out/wanted to!
Some restrictive covenants also states that it is enforceable against any present or future adjoining owner. If indeed your covenant includes this proviso, your neighbours could take action for any breach. I note your one neighbour has no objection and not sure if you have any other neighbour- if you do, then you would lead yourself open to action being taken. However, any such neighbour would either just write to you (and you could then get rid of the hens and that would be it) or the neighbour would have to Court action against, which is going to be very expensive and would not imagine anyone wanting to waste such money).
In short, as long as the hens don't cause a nuisance, I don't think you have
anything to worry about.
I hope this assists and sets out the legal position.