Very generally, once you put something on the Internet, it is very difficult to undo. While some legislations grant you some right to delete your private information or similar, there is no universal right to delete your content.
Specifically, when you post something on Stack Exchange, you do so under a Creative Commons licence. The reason for this is that this site is supposed to be a repository of knowledge and wouldn’t work if people could arbitrarily delete their stuff. You retain a right to have your name disassociated from your posts though (but I presume that this is not your issue). Thus, if you so wish, forfeit the right to delete your content when you post it. You are only granted a certain right of self-deletion so you can clean up after yourself. But:
- You cannot delete your questions once they have an upvoted answer. (Also see this FAQ.)
- You cannot delete accepted answers.
- You cannot delete chat messages older than two minutes. Also see this declined feature request on Meta SE: Allow owner of message to delete them in chat.
Finally in the specific case of comments moved to chat, your comments are already deleted. They continue to exist in another form as chat messages, but then this is the least prominent form of content on Stack Exchange anyway. Also almost everything that has been on the Internet for a certain time persists in some archive. Finally, there usually should be no pressing reason to delete such a message:
- If you posted something rude or otherwise bad, you shouldn’t have done so in the first place (and deleting it doesn’t make you less accountable for it).
- If you posted something that is now obsolete, there is no shame in that.
There are some rare exceptions, e.g., if your comment contains sensitive information due to some accident or similar. In this case, please flag the original post for moderator attention and specify the message and provide a good reason why it should be deleted.