Can an employer terminate an employee that suffers from trypanophobia, which is defined as a fear of needles, without providing a reasonable accommodation to that employee?

Yes. At least, that is the way the U.S. Court of Appeals for the Second Circuit answered this question. In Stevens v. Rite Aid, No. 15-0277 (2d Cir. 2017), the Second Circuit reversed a district trial court verdict that found Christopher Stevens had been the victim of disability discrimination when his employer terminated him for refusing to administer vaccinations to customers because of his fear of needles. The Second Circuit decision overturned a jury verdict in favor of the plaintiff, awarding Stevens back-pay damages of $485,633, front-pay damages of $1,227,188 to cover a period of 4.75 years, and non-pecuniary damages of $900,000, later reduced to $125,000 when the plaintiff agreed to a remittitur. Judgment was entered on Jan. 27, 2015.