If we were to classify Roger Chillingworth's sin under the scope of the seven deadly sins, we could conclude that his most mortal sin is certainly wrath.
As you know, theologically speaking, humans may commit two kinds of sins: Venial sins are the sins that could be classified as "minor" since the degree of damage to others or to self is not too significant. A venial sin is not meant to destroy your life, nor your possibilities of leading a life of grace. It is a fixable kind of miscue.
Contrastingly, Chillingworth purposely and maliciously inflicts pain and terror in both Hester and Dimmesdale as a result of the intense wrath that he feels as a result of Hester's affair with Dimmesdale. Even though Chillingworth is presumed dead by the time Hester and Dimmesdale get together, Chillingworth still cannot forgive Hester for having a child with Dimmesdale and for sparing him (Dimmesdale) from being judged by the congregation the way she is judged daily.
The intensity of Chillingworth's wrath has resulted in that Dimmesdale and Hester's lives are in consistent torment, unjustly and unfairly. All Chillingworth is trying to do is enhance his own ego...or is it simply make Hester miserable? Wrath would then fall under the category of a "mortal" sin. A mortal sin, theologically speaking, is one which takes you completely away from grace because the degree of damage that you inflict on yourself or others is irrevocable.
Therefore, from that theological perspective, Chillingworth's mortal sin is the sin of wrath, and all the other horrid results that come as a result of a wrath that spirals out of control.