Short answer. Sometimes, but carefully. Article 706 of the Civil Code lets a person injured by a private nuisance abate it by removing, or if necessary destroying, the thing, without committing a breach of the peace or doing unnecessary injury. It is a narrow self-help remedy, not a licence to take matters into your own hands freely.
What the law says
Any person injured by a private nuisance may abate it by removing, or if necessary, by destroying the thing which constitutes the nuisance, without committing a breach of the peace or doing unnecessary injury.
Civil Code, Article 706 — Extrajudicial Abatement By Injured Party. Read the full provision →
The law does allow self-help, within strict limits
Article 706 gives an injured person a real but bounded power. Any person injured by a private nuisance may abate it by removing, or if necessary, by destroying the thing which constitutes the nuisance, without committing a breach of the peace or doing unnecessary injury. Read the conditions carefully, because they are where most people go wrong. You must actually be injured by the thing; it must genuinely be a private nuisance; you may destroy only if necessary and only to the extent needed; and you must do it without breaching the peace or causing unnecessary damage. Step outside those limits and your "abatement" becomes your own wrong, exposing you to liability.
It has to be a real nuisance, and injure you
A nuisance in law is not merely something you find annoying or unattractive. It is a condition that injures or endangers health or safety, offends the senses, or obstructs the use of property, in a way that unreasonably interferes with your rights. A neighbour's ugly fence, a tree you simply dislike, or a lawful use of their own land that merely irritates you is not automatically a nuisance you may destroy. Misjudging this is costly: if the thing turns out not to be a nuisance, you have damaged another person's property without justification and must answer for it. The stronger and more objective the harm to you, the safer the ground for abating.
The procedure the article insists on
The provision does not end with the words quoted above. It also requires that the procedure for extrajudicial abatement of a public nuisance by a private person be followed. That means abatement is not a free-for-all; there are steps meant to ensure you are entitled to act and that you act with restraint, including demand and the avoidance of unnecessary destruction. Skipping the procedure undermines the very protection the article offers. Doing more damage than the situation requires, or acting in a way that provokes a confrontation, defeats the defence and turns the remedy against you.
Why the judicial route is often safer
Self-help is tempting because it is quick, but it puts the risk squarely on you: you decide, at your peril, that the thing is a nuisance and that destroying it was necessary and proportionate. If you are wrong on any of those points, you may owe damages and could face other consequences for the manner of your conduct. Going to court to have the nuisance abated shifts that judgment to a neutral forum and removes the danger of overstepping. Where the harm is serious but not an emergency, restraint and a proper complaint are usually the wiser path than tearing something down yourself.