Chillingworth believes that the guilty person must be outed to receive just punishment for his crime. However, Chillingworth also seeks revenge for the personal crime committed against him, i.e. sleeping with his wife. Ultimately, it is the second reason that gets the best of him. You could say that the first reason is a pure reason - justice for justice sake, even justice for Hester's sake giving her a partner in crime to share the burden. But Chillingworth's second reason is purely selfish; it has to do with pride. Pride is the crime of Satan himself, and therefore Chillingworth's second reason/justification is purely evil. It is this evil that consumes his and transforms him.