If you want to clear the list of last typed commands, follow these steps:
(Step 1 and 2 are important, don't skip them!)
Undock the console (click on the icon in the bottom-left corner, ).
(if you don't see , but , then hold the mouse pressed for a few seconds to get the desired icon)
Press Ctrl + Shift + J to open the console for this console. (On OSX use Cmd + Option + i)
Go to the Resources tab, "Local Storage", chrome-devtools://devtools.
Right-click on the item with key "consoleHistory", and choose "Delete".
Done! You may close the new console, and then dock the previous one if wanted. The console history will be gone when you reload the console.
If you just want to clear the console log (not the commands), just press Ctrl + L.
You could also use Incognito mode if you don't want to keep the list of commands you're going to type.