At present, as far as I'm aware, you can clear all history by going to Settings > Clear Browsing Data and then choosing "everything". From within Chrome that is. On the other hand, you can use Incognito mode, which doesn't store history at all.
At present, there is no automatic function for deleting your history in Chrome, such as "clear history on program exit" option. Annoying, but then Chrome is purposefully a barebones browser. You can, however, vote for this feature to implemented in a future release here:
http://www.google.com/support/chrome/bin/stati c.py?page=suggestions.cs
Or just use another browser, like Firefox.