Why does Hester decide to speak to Chillingworth after so many years?Chapters 9 - 15 of the book.
I suspect that Hawthrone set this up so that they could meet in Chapter 17. I have always viewed this as the pivotal chapter in the novel. It is there that the two lovers meet for the first time in 7 years. It is there that they "touch" each other, where Hester reveals her deception, and where Dimmesdale accepts her in spite of it. But this most important thing is that it is here that they discuss their "sin" and what it has meant to them. It is here that Hester tells Dimmesdale, "What we did had a consecration of its own. We felt it so." We see what we may have suspected: Hester accepts the social aspect of her sin, but it is clearly not internalized as it is in Dimmesdale.
I think this is the real reason for their meeting. Certainly it is important on the plot level, but Hester's decision to speak with Dimmesdale, and their actual conversation, does a lot more than express her concerns about Chillingworth.
Hester is concerned over Dimmedale's deteriorating health. She has seen how Chillingworth is torturing him mentally so she decides that she must break her promise to Chillingworth and reveal his true identity to Dimmesdale. Before she does this, she decides she will tell Chillingworth that she is going to expose his identity to Dimmesdale and that's why she must talk with him face to face.