One of our employees has posted negative commentary about his working conditions on social media. Can we discipline her/him for that?

It may be an unfair labor practice, in violation of the National Labor Relations Act, to discipline an employee for complaining about working conditions. 

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Employers should seek competent legal counsel in such instances, because the remedy they may be forced to afford the employee could include reinstating a terminated employee to the same position and paying the employee all lost compensation.