Is it against the law for a company to only hire english speaking US born employees?

In short, it depends on the nature of your employer’s business, but you may have a viable federal employment discrimination claim.  You should discuss the problem with a plaintiff’s employment attorney – s/he will know if you also can avail yourself of the protections of state and/or local anti-discrimination statutes.

Title VII of the Civil Rights Act of 1964 (Title VII), prohibits employment discrimination based on race, color, religion, sex, or national origin.  It is illegal to discriminate against an individual because of birthplace, ancestry, culture, or linguistic characteristics common to a specific ethnic group.  A rule requiring that employees speak only English on the job may violate Title VII unless an employer shows that the requirement is necessary for conducting business. If the employer believes such a rule is necessary, employees must be informed when English is required and the consequences for violating the rule.  Your store owner did state a business reason for imposing the english-only restriction, however an impartial fact-finder – at a goverment agency or in a court of law – could reject his purported grounds in the face of conflicting evidence.  

Although the Immigration Reform and Control Act (IRCA) of 1986  requires employers to assure that employees hired are legally authorized to work in the U.S., an employer who requests employment verification only for individuals who appear to be or sound foreign, may violate both Title VII and IRCA.  Additionally, in some circumstances, employers who impose citizenship requirements or give preferences to U.S. citizens in hiring or employment opportunities also may violate IRCA.