It's not even theorized it exists in the real world even in an awful socialist country like France. Les Tribunaux de Commerce ( Commercial Courts) which arbitrate disputes between companies and contracts, are already private.

You can very well imagine a world based on contracts rather than thousands of useless laws, arbitrated by private courts specified at the beginning, when the contract is signed. Except for criminal cases maybe everything can be private. And even for criminal affairs I'm sure the free market would find a way to deal with it of better quality compared to public courts.