I basically found that it depends on each run.  Chafing from my bra (all 20 brands I have) is just part of the norm.  During runs over 10 miles, I do apply vaseline to where I normally chafe.  That helps!  I don't normally chafe if the run is under 8 miles. 

I would try going to your local running or athletic store and get fitted.  80% of women are wearing the wrong size bra just walking around, of course this is going to cause more difficulty when you are active!  It sounds like there might be too much bounce in your bra - either your band or cup size (or maybe both) are too big, moving around and causing chafing. 

Also, maybe try washing your bra with every use.  If there is any lingering bacteria from your sweat, that is definitely NOT going to help already irritated skin.

Hope this helps!