Battery-Full indicator LED
You can connect it like this: 







simulate this circuit &ndash; Schematic created using CircuitLab

The /CHG pin will sink up to 5mA with less than 400mV drop so it will definitely turn any LED off.  Here Vusb is "IN" on the bq2423x (5V power from the USB bus). 

The /CHG pin is the drain of an N-channel MOSFET (source is grounded) so it either pulls the output low, or it is turned off and the output can assume any value of output voltage (from 0V up to the supply voltage of the chip). 

When the battery is charging the MOSFET is "on" and it shunts the LED, so the current flows through R1 to ground through the chip so the LED remains dark. When charging is complete the MOSFET turns "off", allowing the /CHG output voltage to rise to 2-3V depending on the LED, and the LED illuminates.