In chapter X of Nathaniel Hawthorne's The Scarlet Letter, titled "The Leech and his Patient" we find out about the relationship between Chillingworth and his patient, Arthur Dimmesdale.
The relationship is co-dependent in that Dimmesdale's health is so weak that any help in ailment is very important. Chillingworth, with his knowledge of herbs and cures, is the perfect man for him.
Meanwhile, Chillingworth is highly suspicious of Dimmesdale because, although the man holds a near-sacred position of trust and morality in the settlement, something very odd is gnawing at his conscience, and his ailment is in no way physical. This latter fact Dimmesdale even volunteered to Chillingworth.
But who art thou, that meddlest in this matter?—that dares thrust himself between the sufferer and his God?”
From that point on, Chillingworth begins a quest to find out what lurked within Dimmesdale heart. Chillingworth knows that whatever Dimmesdale has done is an indiscretion of the flesh; of the heart. This is evident when Chillingworth says the words:
He hath done a wild thing ere now, this pious Master Dimmesdale, in the hot passion of his heart!
Therefore, Chillingworth definitely suspects that Dimmesdale's issue has to do with something impure. His excitement about the issue is accentuated by the fact that Dimmesdale is a holy man in the eyes of the people.