In Chapter 4, what does Chillingworth ask Hester to promise? Why does she agree?
Chillingworth asks Hester to promise that she will never betray his identity to anyone. In the interest of fairness, since she has chosen to keep the name of her lover secret, Hester must likewise honor his desire for anonymity. Chillingworth orders Hester not to betray him by word, sign, or look.
When Hester questions Chillingworth about his motives, he answers cryptically. First, he maintains that he prefers to stay anonymous so that he will not "encounter the dishonor that besmirches the husband of a faithless woman." Then, he admits that there may be other reasons; however, he asserts that he need not share those reasons with her. It is enough that it is his "purpose to live and die unknown."
Hester agrees to do what Chillingworth says, only because he threatens repercussions against Reverend Dimmesdale (Hester's lover) if she ignores his injunction not to expose him (Chillingworth): "Shouldst thou fail me in this, beware! His fame, his position, his life will be in my hands. Beware!"
Essentially, Chillingworth threatens to hurt Hester's lover. This is a little disingenuous of him. Remember that, earlier, he had promised he would never hurt the man who got Hester pregnant:
Yet fear not for him! Think not that I shall interfere with Heaven's own method of retribution, or, to my own loss, betray him to the gripe of human law. Neither do thou imagine that I shall contrive aught against his life; no, nor against his fame, if as I judge, he be a man of fair repute. Let him live! Let him hide himself in outward honor, if he may! Not the less he shall be mine!"
Yet, now, when he wants to protect his reputation, Chillingworth has no problems with threatening harm upon Hester's lover. In this chapter, Chillingworth's disturbing threat foreshadows his later sinister involvement in Reverend Dimmesdale's life.
In chapter 4 of Nathaniel Hawthorne's novel The Scarlet Letter, Hester Prynne is inside the prison again where she receives a visit from the man to whom she is married. His new name is Roger Chillingworth, and he enters the prison seeking revenge for what Hester has done to him.
What Chillingworth wishes the most is to know the name of the man with whom Hester has the affair that resulted in her pregnancy and the consequential discovery of her adultery. However, the more he insists on knowing, the less willing Hester is to tell.
Hence, to gain back control of the situation, Chillingworth vows that he will find out who the man is. He also asks, or requires, Hester swear that she will never reveal Chillingworth's true identity, nor will she say that she is or was his wife. In reality, Hester does not have much say in the choice. She is basically forced to silence. She only accepts to do it perhaps out of fear, or because she knows that disclosing this information would make matters worse for everybody involved.
What we do know is that it is her silence what aids Chillingworth to enter the house of Dimmesdale and pose as if he wishes to be his physician only with the intention of harming him.