Unless you specifically opt not to save your chat history, Skype keeps these messages indefinitely. With around 23 million users online during peak times as of March 2010, regrettable chat exchanges probably happen regularly. You can get rid of the offending chat on your side, and even choose not to keep a record of future Skype conversations, but to delete both sides of the chat, you must convince your chatting partner that the record should no longer exist. Writer Bio