My response supposes that you have finished the novel, but you could consider the topics that are relevant to whatever portion of the novel you are familiar with to this point.
Roger Chillingsworth is the husband of Hester Prynn, but not the father of the child, Pearl. Chillingsworth sent Hester to live in Boston ahead of his arrival and when he arrives, he discovers what Hester has done to betray their marriage vows. As his name implies he is "chilly" or cold-hearted when it comes to his treatment of Hester and of Dimmesdale once he discovers that he is the father of Pearl. He is a very knowledgeable man, but he is unemotional and unforgiving. He is determined to seek revenge on Dimmesdale. He is very upset that Dimmesdale actually confesses of own volition because Chillingsworth is cheated of making the public aware of Dimmesdale's sin, thus publicly destroying the once holy man.
A journal entry for Chillingsworth would have to address the anger and shame that Hester's actions have brought upon him. He never comes forward to acknowledge their relationship and he never attempts to understand what happened from Hester's point of view. Chillingsworth's journal would also show his extreme hatred for the unknown man who is the father of Pearl. Even once he knows, his heart is not softened. In fact, he comes to eventually live with Dimmesdale in the position of a healer, but his ultimate plan to drive the guilt further. He is hoping to create a breakdown in Dimmesdale. He only succeeds in driving him to his public confession, which is a bit of let-down for Chillingsworth. This is something that would be explored in his journal. How does he feel once Dimmesdale is dead? Why does he too fall ill? Why does he leave his wealth to Pearl? What motivates him through the entire story?