Why is Hester afraid of the drink Chillingworth offers her?

Hester believes the offered medicine might be poison. She believes that Chillingworth wants to kill her.

“I have thought of death,” said she,—“have wished for it,—would even have prayed for it, were it fit that such as I should pray for anything. Yet if death be in this cup, I bid thee think again, ere thou beholdest me quaff it. See! It is even now at my lips.”