Solved! Go to Solution.
Let me summarize the discussion in this topic so we can close this topic:
To delete the local (!) chat history in a conversation do the following:
NB: This will only delete the local chat history. If you log in to Skype from a different device the chat content will be synced there. This is how Skype chat sync is designed currently.
Some expert said "we have to wait for few more months as they will add this function later"