It's entirely possible to create a big private monopoly in a free market, for example, through first mover advantage, mergers and buying out competition.

Standard Oil, for instance, established an effective monopoly in a highly laissez-faire market. The means by which they did so were not necessarily unethical or illegitimate, but this does not change the fact that having achieved this state, they were in a position to prevent any other companies from reaching a point where they could offer meaningful economic competition, and could enforce exploitative profit margins if they so chose.