I would start by approaching your neighbor and seeing if there is a way to resolve the matter amicably. Be reasonable and level-headed in your broaching of the subject.
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I agree with what counsel has said on this topic, although legally you could remove the mailbox from your property. Before ever taking such action, you should be sure you know exactly where the property lines are, and that his mailbox is not on a public right of way. Assuming it is, in fact, on your property, the best solution is for him to voluntarily move it after having a conversation with you. Judicial action is also a potential method of resolving this dispute, although very expensive in the context of a mailbox. One thing to note, however, is that if you do nothing, your neighbor could eventually become an easement holder relative to the mailbox. Good luck!