Click on “Privacy” tab, and click “Delete All Chat history” button, in result all of your chat history records will get deleted that includes messages, calls, voice/video messages, SMS, text messages, file transfer history. To delete entire Skype chat history, click the main “Skype” menu > “Preferences…”. When done click the “Save” button to save the settings. Click on the drop-down menu under “Keep history for” choose the option that allows keeping Skype history for a specific time like three months, one month, two weeks, forever or no history at all. On the same window, you can also choose to stop recording history or keep the history of a specific period. You can use backup later to transfer history to another computer.
You can backup your Skype history if the reason for deleting history is you are selling your PC.
Note: Make sure you want to do that because all your Skype conversation including messages, voice message, SMS, Calls will be deleted. Hereunder privacy settings click on “Show advanced options” button and there click on “Clear history” and that’s it. However, you can delete your entire Skype chat history in Windows by going through its menu “Skype” > “Privacy”.
I could not find how to delete chat history for a single contact on PC, except you open the main.db file in a viewer and delete specific messages from it.