In chapter 4 of The Scarlet Letter, why does Hester react the way she does to Chillingworth's medicine.
Chapter 4 of The Scarlet Letter, titled "The Interview", narrates how, after returning to prison, Hester was in such a state of nervousness that she was put under watch. This is, of course, because she had just seen Chillingworth from the scaffold. Seeing her presumed dead husband under the current circumstances where she is must be the biggest terror that Hester could experience.
To make things worse for Hester, it is Chillingworth whom the jailer summons to care for Hester, since Chillingworth had entered the settlement registered as a "practitioner" of medicine.
Since Hester is now dependent on Chillingworth for her daughter's health, and her own, she knows that she is the perfect target for him to exact his revenge for the adultery that Hester has committed. Hence, when the man hands a draught made for the child, it is obvious that Hester would think that he would poison her and her child as payback.
Hester repelled the offered medicine, at the same time gazing with strongly marked apprehension into his face.
“Wouldst thou avenge thyself on the innocent babe?” whispered she.
However, Chillingworth does nothing of the kind. In fact, he takes the blame of his anger away from Pearl to replace it back on Hester's conscience. Even he also gives her a draught for her own health, he is also clear in that letting Hester live a life of misery is a better revenge than to kill her.
Dost thou know me so little, Hester Prynne? Are my purposes wont to be so shallow? ...what could I do better for my object than to let thee live,—than to give thee medicines against all harm and peril of life,—so that this burning shame may still blaze upon thy bosom?”
Therefore, although Hester has good reasons to doubt Chillingworth, it is also true that Chillingworth is better off seeing her suffer than seeing her buried. If she died, he would never get to know what he really wants to know: who is Pearl's father and why is Hester keeping it a secret to the point of sacrificing her life forever.