Chillingworth pretends to be a concerned doctor, caring for Dimmesdale. He becomes Dimmesdale's friend and confidant, using that position to find out that Dimmesdale is Pearl's father and is suffering from his secret sin. The narrrator hints at the possibility that Chillingworth is somehow making Dimmesdale sicker. Also, it is clear that Dimmesdale is unsettled about Chillingworth's "friendship" because he admits to Hester that he hates Chillingworth.
In this eNotes Educator's opinion, the relationship between Chillingworth and Dimmesdale can be summed up in one of the chapter titles: "The Leech and his Patient." Chillingworth, of course, is the "leech." A leech, at that time, would have been a reference to a doctor. It has come to be known as a negative term, but wouldn't necessarily have been known that way at that time. Dimmesdale, of course, is the "patient." Chillingworth, in an effort to find out the truth (and inflict the most evil possible), becomes Dimmesdale's doctor.
We must, however, delve deeper into the relationship discussed in this chapter. A doctor is supposed to help the patient. However, this doctor certainly does not. In fact, this doctor has it out for his patient, Dimmesdale. Why? Because Dimmesdale has impregnated Chillingworth's young wife. Chillingworth, therefore, is out for revenge. What a perfect way to hide revenge than to be the "doctor" to a sick "patient." Now, we also must admit that the reason why Dimmesdale is so frail all of the time is one word: guilt. However, there is only one physician that can heal Dimmesdale, and that is a heavenly one.
In conclusion, it is important to remember what has already been discussed by other educators in regards to these two men's relationships to Hester (the main character): Chillingworth is Hester's husband and Dimmesdale is Hester's love.
Dimmesdale is Hester's true love and Chillingworth is Hester's true husband. Chillingworth tries to seek revenge on Dimmesdale by torturing him and making his conscience fill with guilt. Dimmesdale's does not trust Chillingworth. They both secretly hate each other.