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:
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.