Yes, please use a dedicated charging IC for anything Li-ion. Handling the charging properly is described in the info RoGeorge gave, and still it's just scratching the surface. A Li-ion battery is not as easy to handleand forgiving as a NiCd or NiMh battery - if you were used to these, forget about that.
Purely from a rhetorical standpoint, you can, more or less, charge a Li-ion battery with just a voltage source and a series resistor.
Still, you need to make sure your voltage source is 4.2V within about 50mV - which will already require a more elaborate voltage source than you'd probably want to care about if you're thinking of cheaping out on a proper charging IC.
Alternatively, for safety reasons, you can of course settle for a lower max voltage. For instance, 4V regulated within +/-5% (which should not be too hard to do with a cheap linear reg) should do. You can go for 3.9V for a bit more margin.
The issues though with this approach are the following:
- Since you'll have to limit the max voltage to lower than 4.2V, you won't get a full charge.
- Since the charging current will vary with the cell voltage, if the cell is fully discharged, it will start with the max. current and the current will gradually decrease. So to keep the max. charging current within specs for the cell, you'll have to select the series resistor appropriately (typically, a fully discharged Li-ion cell should be around 3V, so if you use a 4V source, your starting current with be (4-3)/R = 1/R. The downside is that charging the battery will take much longer this way (due to the current dropping as the cell charges up). Also, starting with the max current is not a good idea if the cell is in deep discharge state. Dedicated ICs do check the cell voltage before starting to charge, and if in deep discharge, they'll either decide to fail (if the cell voltage is too low to be safe), or "trickle charge" it with a low constant current until it raises above a certain threshold (about 3V), past which they'll switch to a higher current. With a simple series resistor approach, attempting to recharge a deeply discharged cell may result in something not pretty.
- Dedicated ICs do detect an end of charge condition and stop charging at this point. A simple series resistor approach won't, and will keep "trickle charging" the cell until you unplug it from the charger. That's usually guaranteed to not end up very well after a while (many batteries will tend to swell).
So, while this could work if you really have nothing else at your disposal and must charge a Li-ion battery in some emergency situation, under supervision, I would certainly not recommend doing that routinely and leaving it unsupervised.