Bad work environment?:
It certainly can if you have the right attorney.  Racial remarks are a form of sexual harrassment and the company, along with the person, and the supervisor can be held liable for it.  The USA has laws in place that prohibits anyone from having to work in a hostile work environment.  The first step you need to take is to contact the human resource (or personnel) department of your workplace and tell them your story.  You need to write down what was said, the date it was said if you remember, and who was, if anyone, a witness when the person said it.  If the human resource department does not do anything about this, go above their head and contact the main office.  If this option is not available to you, I would consult with an attorney to determine what the next step is you should take. 
Be sure to have with you a copy of the complaint, if one was given to you, to take to the attorney.