A derogatory personal comment was made about me in my presence on a conference call on Thursday. After the laughter died down, the person that made the comment admitted they should not have made the comment and they were just joking. The comment has troubled me since. On Friday, I contacted the HR Department of our company and they want to discuss the issue in detail. However, I left early for the day due to not being able to concentrate on work. I have decided to resign on Monday, regardless. I will not be comfortable working in the presence of the person that made the comment nor the others that were on the conference call. All the projects that I work on involve at least a subset of this group. I have read about "constructive termination" where a person quits because the work environment has become intolerable. Would this qualify as such?

I believe I've answered this on another board. No, a single comment is not sufficient to define "intolerable working conditions". This would not qualify as a constructive termination and it is highly unlikely that unemployment would be granted were you to resign over this issue.