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It's not "automatically" illegal but it certainly can be illegal.
The most obvious thing that comes to mind is that it can be a violation of the ADA, and it sounds like everyone agrees the ADA applies, and your need for a reasonable accommodation.
You probably want to go and visit with a local lawyer that does Employment Law and have them write a letter to your employer asking for the reasonable accommodation and explaining why it is necessary and reasonable. The letter serves another purpose, it can be used as evidence if you do have to sue and the lawyer will draft it and word it with that in mind.
That is the only law that I see this violating.
However, you do have to file a charge of discrimination with the ADA once you know for certain they are refusing the accommodation. You have a short time to do this, as short as 180 days in some situations, and if you miss the deadline then you can never file a lawsuit as you will have failed to "exhaust all administrative remedies".
Please ask any follow up questions you have in this thread.
If you don't have any follow ups and you question has been answered then I'd offer my best wishes to you and ask that you please not forget to leave a Positive Rating so I receive credit for my work.
Of course, as I said, please feel free to ask any follow up questions in this thread. I want to be sure that all of your questions are answered. In addition, once you issue your Positive Rating the question will lock open and you can come back to it anytime in the future if you think of something else.