Without commenting on whether you have a claim for illegal employment discrimination, the answer to your question is yes.
You can sue your employer for discrimination regardless of whether you are employed "at will" or on a contractual basis. The real question is whether the employer laid you off because of your race. If it was for some other reason, it's not discrimination. However, it can be difficult for employers to successfully argue it wasn't discrimination if the person who remained on the job was not as qualified as you, or earned more than you, etc. You should consult with an attorney who will ask you detailed questions about your circumstances and help you decide the best course of action.
An employee without a union or employment contract is an employee at will and can be fired for no cause at all. If discrimination based on race, gender, age, religion etc... is the basis for your firing, you may have recourse.
Good luck to you.
NOTE: This answer is made available by the lawyer for educational purposes only. By using or participating in this site you understand that there is no attorney client privilege between you and the attorney responding. This site should not be used as a substitute for competent legal advice from a licensed professional attorney with whom you have established an attorney client relationship and all the privileges that relationship provides. The law changes frequently and varies from jurisdiction to jurisdiction. The information and materials provided are general in nature, and may not apply to a specific factual or legal circumstance described in the question.