Good information to know - glad you posted.
According to Federal employment laws, you are not required to anwer questions concerning your health -either during a job interview or on a health form. The only health information you should need to submit is a form that goes directly to the medical insurance agency -something the is not in your employment file and something that is protected by HIPAA rights. Unless you are involved in a contact sport (no, nursing doesn't qualify!) your employer should never see this.
Your employer has the right to drug screen you, but not test for anything other than drugs. So, no, you do not have to offer that information no more than you have to tell them you are preganant, homosexual, have mental illness, etc. I hope this helps! ~MM
Did your prospective employer draw any blood in your application process? If so, they probably already know.
Also, in my mind's eye there is a difference between a "chronic illness" and being diagnosed with a disease. Since you are asymptomatic you are not "suffering a chronic illness." That said, what sort of health care facility are you hoping to work for that you think would not understand your diagnosis?
I think what your asking is a moral question, which only you have the answer to.
Best of luck in your decision,
Pro