To delete the local (!) chat history in a conversation do the following:
1.Open the "Recent" tab (iPhone & iPod) / sidebar (iPad).
2.Tap the "Edit" button
3.You will see a red remove icon next to each conversation. Tap it to remove.
Note: 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 (Latest Version only).