pegwatcher:
You cannot properly charge a li-ion with only a constant current source. It must be a two stage charger: First a constant current source and then a constant voltage source.
I charge my lithium's the same way ultrafire chargers do it, using a pnp (wtith an complementary npn) and cutting the voltage / charge every couple of seconds to monitor it's voltage level, it all runs from 5v on an Arduino...