Note: Please read all of this!
To "delete" all of your chats, go to "skype" drop down menu,
"Preferences" > "Privacy" > "Delete History"
Note, this is NOT good enough to then sell your mac.
Skype does not actually delete your chat at all other than to hide it from yourself or casual users.
Your chat is not even deleted and I am not talking about secure delete.
To remove your chat, go to your home folder, Library > Application Support then drag your entire "Skype" folder into the trash, and from the Finder, go to the "Finder" drop down menu and select "Secure Empty Trash"
If you do not do that, you can still find your chat conversations the skype "deleted" via the Privacy Preferences by opening "Application Support" > "Skype" > [folder named after your skype username] > "main.db"
Click the tools from menu and then select options
Then click privacy
Here you will find clear history button
it will clear all history thanx
You can remove all conversations/calls from Recent in sidebar by selecting:
Conversations > Clear Recent...
If you want to remove single item from Recent list, right-click on conversations/call you want to remove and choose Close.
Closing (not deleting!) conversation from Recent does not remove its history so you can find closed conversation later. Of course, you need to have saving chat history enabled in Privacy tab.
There is also an option to delete single conversation from sidebar and history. Please remember that it will remove completely such conversation and it cannot be undone. You can do it either by right-clicking conversation and selecting "Delete Conversation..." or from menu Conversations > Delete Conversation...