What do you think Chillingworth dees when he secretly enters the minister's room? What effect does this incident have on the physician?

I think the best description of this comes from right here on gradesaver. You can link the entire chapter summary and analysis below;

"The end of the chapter brings to light some of what previous foreshadowing promised. Earlier, Chillingworth told Hester that he would be able to know her partner by reading his heart. In the final scene, he is in fact able to read Dimmesdale's heart and know the secret Dimmesdale is hiding. Hawthorne, however, indicates that Chillingworth is surprised by what he discovers, implying that Chillingworth never fully suspected Dimmesdale of being Pearl's father."