On Windows and Mac, you can delete your entire conversation history – including instant messages, calls, voicemails, SMS and sent and received files. It is not possible to delete individual conversations, or the history for just one contact.
Go to Skype > Privacy and under the section called Keep history for, click the Clear History button. This deletes all of your chats and cannot be undone.
If you want to change your history settings, select a new option from the Keep history for drop-down.
Click Preferences > Chats > Clear History.
This deletes all of your chats and cannot be undone.
On Linux, you can choose to delete only certain conversations. To delete your chat history on Linux:
Open your History and select the events you wish to remove (by dragging, or by selecting individual events)
Right-click and select Delete Event (or for multiple events, Delete Selected Events)
If you want to disable your chat history on Linux:
Click the small Skype icon on the bottom right corner of the screen and select Options > Privacy
From the Keep chat history drop-down, select Disable History
Click Apply and Close