I'm guessing it actually occurs in your .htaccess file or Apache config, not Kohana specifically. First of all, make sure that the example.htaccess file that comes with Kohana is renamed to .htaccess, and you may have to restart Apache.
If you are using .htaccess to hide the index.php part of the path, check to see what the RewriteBase setting is:
RewriteBase /kohana/
If you installed it in the root of your web server (as in production, or using a separate port for localhost), then it should be changed to:
RewriteBase /
This is my own personal most common error in setting up new sites and development environments, by the way. This is also true for CodeIgniter and other related PHP frameworks.
Does your Apache install on the Debian server actually have mod_rewrite? It would be good to confirm that. Here's one way to do that.
Further diagnosis to see if it is Kohana or Apache's fault includes adding back in the index.php portion of the path. In your case, try http://localhost/kohana/index.php/index. Finally, I have to agree with sarfraz above that naming your controller "index" is just begging for trouble. My own convention is to call it "home" and to edit the default route accordingly.