As the Petition in NLRB v. Murphy Oil USA puts it, the issue is:
Whether arbitration agreements with individual employees that bar them from pursuing work-related claims on a collective or class basis in any forum are prohibited as an unfair labor practice under 29 U.S.C. 158(a)(1), because they limit the employees’ right under the National Labor Relations Act to engage in “concerted activities” in pursuit of their “mutual aid or protection,” 29 U.S.C. 157, and are therefore unenforceable under the saving clause of the Federal Arbitration Act, 9 U.S.C. 2.In other words, can employers enforce agreements that will force employees into individual arbitration and forego collective or class actions?
The Supreme Court has been very arbitration-friendly over the years, but often in closely divided cases. Justice Scalia was one of the voices in the narrow majority. This one could come down to President Trump's appointment (assuming (s)he gets confirmed in time to hear the case).