If a defense atty discovers incriminating (convicting) evidence about a client after he and the state rest, is he legally bound to advise the judge?

I knew of a high profile attorney who declined to take on a client because he was convinced of his guilt. In the piece of fiction I'm writing, the lawyer is convinced of the client's innocence...until just after she and the State have rested, and prior to closing arguments. Setting aside the moral issue of arguing for acquittal in a capital case when one is convinced of a client's culpability, is there a statue of any kind REQUIRING the disclosure of that damning evidence? The court system in the story is in the city of Chicago, if that has bearing on the answer. Thank you, thank you, for your time!