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Chomsky follows Marx in opposing the private ownership of the means of production, which he believes permits "elite groups" to :"command resources, based ultimately on their control of the private economy," and ends up excluding the public from "basic decisions concerning production and work."3
Let's stop right there. What he means is hard capital: machines, buildings and so on. One would think that if private persons and business concerns cannot own these things, the state will do so. We call that state socialism. Chomsky apparently is against that too.
So, if the state isn't going to own income-producing property, and private concerns are not going to own it, who is going to own it? Apparently, and this all very fuzzy, the means of production will somehow be collectively owned by the workers themselves, wherein we arrive at the silly concept of anarcho-syndicalism. Instead of greedy capitalists owning the corporation, the workers themselves will own it. But it will not be ownership in the form of individual shares that can be sold. That's capitalism.
No, he favors a vague and ill-defined form of collective ownership that the workers will figure out as they bumble and stumble along towards bankruptcy. As Mises writes in Socialism, "as an aim, Syndicalism is so absurd, that speaking generally, it has not found any advocates who dared to write openly and clearly in its favor."
Details aside, imagine how this syndicalism idea would have worked out recently in America. Let's say the workers had the privilege of owning Enron. Giddy syndicalists seem to view ownership of business concerns as always and everywhere a good thing.
But ownership also implies risk and liability, liability for debts and lawsuits. After Enron collapsed into a pile of incomprehensible derivatives, how many workers there wished they co-owned Enron? Under current law, employers are responsible for the torts and contract breaches of employees. How many workers would want to bear that risk?
https://mises.org/library/chomskys-economics