Sorry, my mistake. I’ve now corrected it.
The MCP73831 has 3 charge modes. The charge LED will be on in all three modes but the current won’t always be the programmed charge current. You have to make sure you’re measuring during Fast Charge Constant-Current mode.
Summarising the datasheet, the modes are:
Preconditioning: If the voltage at the V BAT pin is less than the preconditioning threshold, the MCP73831/2 enter a preconditioning or Trickle Charge mode. It supplies a percentage of the charge current (established with the value of the resistor connected to the PROG pin) to the battery.
Fast Charge Constant-Current Mode: The programmed charge current is supplied to the battery or load. This is the mode you should be in to measure the charge current.
Constant-Voltage Mode: When the voltage at the V BAT pin reaches the regulation voltage, V REG, constant voltage regulation begins.
(Charge Termination, charge LED off): The charge cycle is terminated when, during Constant-Voltage mode, the average charge current diminishes below a percentage of the programmed charge current.
I measured the charge current of one of my Arduboys, as seen through the USB port, using a USB breakout board I made. I’ve changed the programming resistor on this Arduboy to 8.2K. The measured current was about 123mA. The formula says it should be 122mA.