Chase is a bit finicky, they like to see fairly long history with near spotless reports (whoever they pull that is). If you can't get the lates removed, you might have to wait at least another 6 months. Chase also seems to like fairly thick credit files, showing the person has handled credit well with more than a couple accounts. At least this is what I've read about them for years. I won't waste an INQ on them for some time and my reports are spotless with 16 accounts showing, one of them being an AU Freedom.
I don't think you need to be spotless, but maybe give it some more time. I was approved for Chase Freedom today. I have 7 accounts with lates, ranging up to 150 days late, but the lates are over three years old. 10 months might be too recent.
Starting Score: ~500 (12/01/2008)
Give it more time. Last thing you want is to be given a low limit card that won't grow as your credit improves. 
Pretty much all the major credit card companies are going to cringe at a late within the last year. Let it age a bit more.