You can delete chat history on Skype. Skype archives your chats for you and stores them locally on your computer, if you have enabled this option. Chat histories are not stored anywhere on the Skype network. No one someone, no one else will ever be able to see any of your chat histories except you and the person you are chatting with.
Chats are archived as a convenience to you, so that you can easily keep track of your chat conversations on Skype – think of it as sent mail for Skype.
To enable or disable this option go to Skype -> Preferences -> Chat and select your choice of chat history settings.
To view archived chat sessions for a specific contact, select the contact from your Contact List and go to Contacts -> View Chat History. A browser window will open showing your previous chat sessions with the selected contact.
You can clear your chat history by selecting Delete All Chat Messages under the Chat menu.
Go to Tools ->Options -> IM & SMS -> Show advanced options.
Please note that calls are not archived and therefore won’t be shown in chat history.
If you want to backup your chat history or move it to another computer you can find it in a folder with the same name as your Skype Name in username/Library/Skype.