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.
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