My dog provides me with emotional support. Do I have a right under the ADA to have my dog with me on the job?

This is not a yes or no answer. In terms of employment under the ADA, the US Equal Employment Opportunity Commission (EEOC) is the federal agency that creates the regulations (Title I) related to employment. They have not defined service animal in their regulations, unlike the US Department of Justice (DOJ) in its ADA regulations for Title II and III. Instead, the EEOC has made the issue one of reasonable accommodation, the mechanism by which a person with a disability can ask for a change or alteration in the work environment in order to be able to do the essential job functions. In the workplace, an emotional support animal might be a possible reasonable accommodation. However, the employer must decide whether or not it is reasonable to permit the dog and that it would not cause an undue hardship to allow the dog.