While you probably should consult with experienced employment law counsel to evaluate your situation in greater detail, it may be legal to fire you from custer service due to a stutter. The law prohibits discriminating against someone in employment due to a disability (an initial question, therefore, is whether your stutter qualifies as a disability); however, not discriminating consists of making "reasonble accomodations." A reasonable accomodation is some modification of duties or assistive devices/technology which let you do the job, so long as such accomodation is not too expensive or disruptive for the employer. However, if the employee simply cannot reasonably do the job, even with a reasonable accomodation, he or she may be terminated--the law does not require an employer to employ someone who can't perform the duties of his or her job. A stutter could make it effectively impossible to do a customer service job--customers may have difficulty understanding you, may get impatient with you, etc. Therefore, while a stutter would not affect many jobs, like in tech support, graphics, data entry, etc., it might make it impossible to be a CS person on the phone; and if so, termination would seem to be legal.