If there is an unclaimed island in the ocean, can you legally claim it and live there

by law? Say, I find an island in the ocean that has not been claimed by any country. Could I claim the island for myself and then live there and rule it as my own and not be governed by any government? Like since it was never claimed beforehand and thus I am the first person to claim it. Would I be the legal owner and it be mine with no legal system over it?
Could you go to the UN and get them to have international law see it as your own?
 
Theoretically yes.

In reality, the marijuana farmers would see you as you came into the island and shoot you.
 
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