CSS class for view display not being applied
I said IF its D7 bc I could not find what version. I was reading it on my phone. But here's your Drupal 6 answer:

But here's the template suggestions for D6:
http://drupal.org/node/1089642

You can download devel module to get template suggestions as well.

-OR-

Download this module to add css classes to specific blocks:

http://drupal.org/project/block_class