Before labeling a society in which different people are under different laws chaotic and unjust, remember that in our society the law under which you are judged depends on the country, state, and even city in which you happen to be. Under the arrangements I am describing, it depends instead on your protective agency and the agency of the person you accuse of a crime or who accuses you of a crime.
The objections to private law can be puerile. One common claim is that there must be a supreme court, or legal processes would have no end. This is seen false simply by noting that processes can end in other ways. In a free society, there would likely be your court, my court, and if things are still not settled, an appeals court. Every pair of PDAs could use a different appeals court. Two out of three wins. Clearly there's no need for a maximum court ruling over all.
In such a society law is produced on the market. A court supports itself by charging for the service of arbitrating disputes. Its success depends on its reputation for honesty, reliability, and promptness and on the desirability to potential customers of the particular set of laws it judges by. The immediate customers are protection agencies. But the protection agency is itself selling a product to its customers. Part of that product is the legal system, or systems, of the courts it patronizes and under which its customers will consequently be judged. Each protection agency will try to patronize those courts under whose legal system its customers would like to live. - David Friedman, Police, Courts, and Laws - On the Market, Ch. 29 Machinery of Freedom
Another common objection is that private courts would fight it out violently rather than accept arbitration or deal with other PDAs. But PDAs have a greater incentive to negotiate and act peacefully than states. First of all, wars are expensive in money and personnel; PDAs cannot shift costs to hapless subjects like states can. Neither can they simply raise prices like states - their customers would go elsewhere, to more peaceful and reasonable competitors. If worse comes to worse, and armed conflicts occur, PDAs being non-territorial cannot use weapons of mass destruction as states do. Nor do they have the patriotic fervor or the People's Romance to rationalize killing "them" - the demonized people living in "enemy" territory. Thus any wars that do occur are likely to be small and localized, for clear pursposes, and with careful distinction between combatant and noncombatant.