In the Scarlet Letter Chillingworth is living with Dimmesdale because his health recently became bad. But whose idea was it and why?
Roger Chillingworth, "the good physician," considers Reverend Arthur Dimmesdale's failing health to be to his (Chillingworth's) advantage. However, Dimmesdale's friends (presumably men such as Reverend Wilson and Governor Bellingham) ultimately persuade Dimmesdale to avail himself of the doctor's assistance:
After a time, at a hint from Roger Chillingworth, the friends of Mr. Dimmesdale effected an arrangement by which the two were lodged in the same house; so that every ebb and flow of the minister's life-tide might pass under the eye of his anxious and attached physician (125).
...and of course, Chillingworth would have "hinted" this was the ultimate arrangement he desired! -- for this way, he could constantly keep watch over his patient and could
now [dig] into the poor clergyman's heart, like a miner searching for gold; or, rather, like a sexton delving into a grave, possibly in quest of a jewel that had been buried on the dead man's bosom....(129).
Something -- perhaps Chillingworth's intuition? -- is telling him that he needs to investigate Dimmesdale. What better way to do so than to constantly be with him? Ultimately, you as the reader decide whether or not Dimmesdale's friends make a good decision that actually improves the minister's health.