how clear the skype chat history ?
Go to Tools > Options > Privacy
press the button Clear History.
By using the Clear history button, within Skype's Privacy Settings (as explained in the other answer also), you'll remove all chat history from all your contacts.
If instead you only want to remove the history for a selected skype contact, then you can do so be performing these steps:
Sign out from Skype and close Skype.
Backup your skype database "main.db", typically located in something like
AppDatain windows is typically a "hidden" folder, so you might have to first make that folder visible also).
Download the GUI editor for SQLite databases.
Install and launch this downloaded "GUI editor for SQLite databases" and open the "main.db" database (from step "2.").
Search for the record(s) corresponding to the chat messages you want to be deleted (the skype name will the login ID of the user whose messages you want to deleted), and just delete those records.
Close/exit the "GUI editor for SQLite databases".
Restart skype to verify that the chat messages you deleted are indeed gone.
Refer to the video about "How to delete specific Skype messages" for a demo of the steps above.
Be aware: the steps above will delete that chat history on your computer. But these chat messages will still exist on the computer of your Skype contact.