Do you have access to bands (like Superbands or Woody Bands, etc.)? If you do, hang a couple off the chinup bar, hook your knees into the lower loops, and use it as assistance on the chinups. (It's possible that you'll need help getting yourself into position.)
You might have to start with some pretty thick bands (or a few medium size bands).
It works well in translation to regular chinups, despite the assistance, because unlike pulldowns or the assisted chinup machine, the bands don't provide much stabilization... so your 'core' has to work to keep you from swinging around.
As you get stronger, use thinner bands.
p.s. If you try this, be careful not to get in the habit of using too much bounce out of the bottom part of the chinup. The bands will certainly give you some assitance bounce, but don't get in the habit of using it as your main source of momentum. First of all you'll end up swinging like crazy after a few reps, and second when you get to regular chinups, your shoulders will hate you for trying to bounce out of the bottom!
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