Good evening and thank you for entrusting me to answer your question. I am very sorry to hear about your paralyzed vocal chord and completely understand your concerns.
Fortunately, an individual in your circumstance may very well have recourse.
This is because the Americans With Diabilities Act requires employers to provide "reasonable accommodations" to employees with qualifying disabilities. A qualifying disability is a condition which "significantly impairs a major life function." Since talking is of course a major life function, a paralyzed vocal chord that limits an individual's ability to speak for extended periods of time likely satisfies this definition.
Assuming your condition does qualify as a disability, your employer is required to engage in an interactive process with you to determine whether your disability can be reasonably accommodated. A "reasonable accommodation" is any change in the work environment or in the way things are customarily done that enables an individual with a disability to enjoy equal employment opportunities and that does not impose undue hardship on the employer.
Thus, if your employer can move you to a different position or modify your job duties so that you don't have to spend so long talking on the phone, they would be legally required to do so. However, if your employer can demonstrate that to modify your job duties or to "accommodate" you in any fashion would pose undue hardship (defined as significant difficulty or expense), they would be able to insist that you perform what is being requested of you and terminate you if you are unable to do so.
Most employers are eager to avoid litigation, and so if you write a letter to your employer (you will want this to be in writing so there is record of it) indicating that your vocal chord condition qualifies as a disability and you are requesting accommodations, they will likely facilitate your request.
These are the rights available to an individual in your circumstance. You can read more about ADA accommodations here: http://www.eeoc.gov/policy/docs/accommodation.html
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