Update:
console.clear()is available in all browsers
Update: As of November 6, 2012,
console.clear()is now available in Chrome Canary.
If you type clear() into the console it clears it.
I don’t think there is a way to programmatically do it, as it could be misused. (console is cleared by some web page, end user can’t access error information)
one possible workaround:
in the console type window.clear = clear, then you’ll be able to use clear in any script on your page.