Yes, more or less. Since both anarchism and capitalism are theoretical models, it’s hard to claim that any real situation is completely stateless and free-market capitalist. But there are various societies that were, for all intents and purposes, stateless, and societies that implemented anarcho-capitalist “programs” such as private law. Here is a short list:
Celtic Ireland (650-1650)
In Celtic Irish society, the courts and the law were largely libertarian, and operated within a purely state-less manner. This society persisted in this libertarian path for roughly a thousand years until its brutal conquest by England in the seventeenth century. And, in contrast to many similarly functioning primitive tribes (such as the Ibos in West Africa, and many European tribes), pre-conquest Ireland was not in any sense a “primitive” society: It was a highly complex society that was, for centuries, the most advanced, most scholarly, and most civilised in all of Western Europe. A leading authority on ancient Irish law wrote, “There was no legislature, no bailiffs, no police, no public enforcement of justice… There was no trace of State-administered justice.”
Icelandic Commonwealth (930 to 1262)
David Friedman has studied the legal system of this culture, and observes:
The legal and political institutions of Iceland from the tenth to the thirteenth centuries … are of interest for two reasons. First, they are relatively well documented; the sagas were written by people who had lived under that set of institutions and provide a detailed inside view of their workings. Legal conflicts were of great interest to the medieval Icelanders: Njal, the eponymous hero of the most famous of the sagas, is not a warrior but a lawyer–“so skilled in law that no one was considered his equal.” In the action of the sagas, law cases play as central a role as battles.
Second, medieval Icelandic institutions have several peculiar and interesting characteristics; they might almost have been invented by a mad economist to test the lengths to which market systems could supplant government in its most fundamental functions. Killing was a civil offence resulting in a fine paid to the survivors of the victim. Laws were made by a “parliament,” seats in which were a marketable commodity. Enforcement of law was entirely a private affair. And yet these extraordinary institutions survived for over three hundred years, and the society in which they survived appears to have been in many ways an attractive one . Its citizens were, by medieval standards, free; differences in status based on rank or sex were relatively small; and its literary, output in relation to its size has been compared, with some justice, to that of Athens.
— David Friedman, Private Creation and Enforcement of Law: A Historical Case
Rhode Island (1636-1648)
Religious dissenter Roger Williams, after being run out of theocratic puritan Massachusetts Bay Colony in 1636, founded Providence, Rhode Island. Unlike the brutal Puritans, he scrupulously purchased land from local indians for his settlement. In political beliefs, Williams was close to the Levellers of England. He describes Rhode Island local “government” as follows: “The masters of families have ordinarily met once a fortnight and consulted about our common peace, watch and plenty; and mutual consent have finished all matters of speed and pace.” While Roger Williams was not explicitly anarchist, another Rhode Islander was: Anne Hutchinson. Anne and her followers emigrated to Rhode Island in 1638. They bought Aquidneck Island from the Indians, and founded the town of Pocasset (now Portsmouth.) Another “Rogue Island” libertarian was Samuell Gorton. He and his followers were accused of being an “anarchists.” Governor Winthrop of Massachusetts Bay called Gorton a “man not fit to live upon the face of the earth,” Gorton and his followers were forced in late 1642 to found an entirely new settlement of their own: Shawomet (later Warwick). In the words of Gorton, for over five years the settlement “lived peaceably together, desiring and endeavouring to do wrong to no man, neither English nor Indian, ending all our differences in a neighbourly and loving way of arbitration, mutually chosen amongst us.”
The coastal area north of Albemarle Sound in what is now northeastern North Carolina had a quasi-anarchistic society in the mid-seventeenth century. Officially a part of the Virginia colony, in fact it was independent. It was a haven for political and religious refugees, such as Quakers and dissident Presbyterians. The libertarian society ended in 1663, when the King of England granted Carolina to eight feudal proprietors backed by military.
Holy Experiment (Quaker) Pennsylvania (1681-1690)
When William Penn left his Quaker colony in Pennsylvania, the people stopped paying quitrent, and any semblance of formal government evaporated. The Quakers treated Indians with respect, bought land from them voluntarily, and had even representation of Indians and Whites on juries. According to Voltaire, the Shackamaxon treaty was “the only treaty between Indians and Christians that was never sworn to and that was never broken.” The Quakers refused to provide any assistance to New England’s Indian wars. Penn’s attempt to impose government by appointing John Blackwell, a non-Quaker military man, as governor failed miserably.
The American “Not so Wild” West — various locations
Most law for settlements in the American West was established long before US government agents arrived. Property law was generally defined by local custom and/or agreement among the settlers. Mining associations established orderly mining claims, cattlemen’s associations handled property rights on the plains, local “regulators” and private citizens provided enforcement. Yet most movie-watching people are surprised to learn that crime rates were lower in the West than the “civilised” East.
Laissez Faire City
A more recent unsuccessful attempt to start a new country, Laissez Faire City attempted to lease a hundred square miles of land from a third-world State in order to start an anarcho-capitalist society, taking Hong Kong as a guide. When that fell through, some members moved to Costa Rica, where the State is relatively weak, there is no standing army, and what little State interference there can usually be “bought off.” There remain small libertarian communities in the central valley (Curridabat) and on the Pacific coast (Nosara).