It's odd, at work we have about 15-20 Dremels that are quite a few years old, mainly 8200's, all with the Dremel official drill style chuck on them, no issues at all and these things get ABUSED. Recently we ordered four new 8220's for new starters, along with the chucks to go with them. Two of them would not fit at all, even on existing 8200's. Seems their manufacturing has changed.
Having said that, if you've managed to break one of the old style chucks then I don't know what to tell you...