I'm still doing the chair-assisted pull-up exercises, because I'm weak. But here's the progress I've made:
It's cheating (because it's not proper form nor a proper pull-up), but if I grab the perpendicular handles and jump, bringing my knees to my chest I can indeed pull myself up to where the bar is somewhere between my nose and my chin. More importantly, I have the strength to slowly lower myself down from this position.
Mind you, I don't have the strength to do this again for several hours, but it's more than I could do before.
If we're taking proper form into account, then the best I can do is pull myself about 6-8 inches off the ground. Considering that this time last month I couldn't even lift my body off the ground, this is a significant improvement.