It seems that in the Window version of Skype, there is an option to clear chat history. It is supposed to be Tools > Options > IM & SMS > Clear history button but effectively nothing similar is here:

This option is not present on the version that come with my Ubuntu 13.04. In the privacy settings there is this option:

and somewhere in the Skype forum it is said that changing that to Disable History and then restarting Skype will get rid of the chat history. Tried that, don't work.

Searching a bit I found that you have to eliminate some file in the Skype directory; I did that from the directory I have:

cd $HOME/.Skype/my_skype_name/ 

rm chat*.dbb user*.dbb 

...still no go. Before I get rid of all the .Skype directory and re-configure all Skype, is there anyone that know how to do it? The content of the directory is:

alert2048.dbb       chatsync             httpfe           msn.db-journal

alert4096.dbb       config.lck           keyval.db        msn.lock

bistats.db          config.xml           keyval.lock      profile16384.dbb

bistats.db-journal  contactgroup256.dbb  main.db          sms512.dbb

bistats.lock        dc.db                main.db-journal  transfer256.dbb

call256.dbb         eas.db               main.lock        voicemail

callmember256.dbb   eas.db-journal       msn.db           voicemail256.dbb

Removing all other *.dbb doesn't work, either.

Lesson: never put sensitive data on a Skype chat.