Lithium batteries are particularly intolerant of incorrect charging; simply connecting the battery to USB would be a good way to generate a fire or explosion (no, I am not kidding).
Since Li technology batteries are ~3.6V, you need either a 3.3V arduino variant with an LDO regulator, 2 cells, or a boost regulator.
There are ICs available specifically designed to charge Li cells from USB voltages (MAX1555, etc).
-j