An employee who uses racial slurs at work may attempt to argue that requiring him to refrain from doing so violates his free speech rights.
However, the California Supreme Court decision in Aguilar v. Avis Rent A Car System, Inc. confirmed that you can order employees to stop using derogatory racial and ethnic slurs in the workplace. The California Supreme Court ruled that the right to free speech guaranteed by the First Amendment does not protect racial slurs.1
If you do not create a work environment free from harassment on your own, judges have the power to force you to do so.
1. Aguilar v. Avis Rent A Car System, Inc., 21 Cal. 4th 121 (1999), cert. denied May 22, 2000