You can clear all of the history by going to Tools -> Options -> Privacy > Advanced and clicking on "Clear Chat History". However there is no way to delete the history for just one contact, you may be able to look through the stuff Skype saves on youer computer and find individual logs. I think they are saved somewhere in one of these folders:
%APPDATA%\Skype
%APPDATA%\skypePM
The 'SkypePM' folder seems to contain a bunch of '.ezlog' files which I have no idea what they are for, they are not human readable, maybe only by Skype. In the 'Skype' folder there are a bunch of 'chatmsgXXX.dbb' files where 'XXX' is a number which could also be logs of some kind.
I would make backups of them then try and deleting them and see what happens. If it works you can delete the backups or restore them if it doesn't. Otherwise you just have to clear the entire history.