Off the top of my head I forget what kinks I ran into when trying to get CSS to load on my development server. I'll try and come up with things I remembered and let you know if I do.
One thing in Chrome that I tend to have to do (probably why firefox is better in this case) is I have to clear my browsing data. That way the files propagate through to my browser. Here's how to do that:
Did you run python manage.py collectstatic? and restart your local development server with python manage.py runserver?
Cheers,
JJ